Search results for: design equation

Authors: Ali Safdari-Vaighani

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Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method.

Keywords: basket option, jump diffusion, ‎radial basis function, RBF-PUM

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Authors: Martina Maria Keitsch

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Critical Design (CD) confronts traditional design practice. Instead of reproducing and reinforcing contemporary perceptions of products and services, CD seeks to challenge them with the goal to stimulate debates and visions on societal innovation. CD methods comprise, among other narratives and design of critical objects. The oral presentation is based on a study that discusses concepts, methods, and applications of CD links CD to traditional design, and identifies CD benefits and challenges for design research and practice. The objective of the study is to introduce CD as an alternative for design researchers and practitioners supplementing commercially oriented design approaches. The study utilizes a literature review on CD concepts and methods based on current publications and online documents and illustrates CD practice with help of selected case studies. Findings of the study indicate that CD contribute, among others, to create new societal roles for designers, foster innovative relationships between designers and users, and encourage creativity through imaginative aesthetics.

Keywords: critical design, postmodern design theories, narratives, rhizome

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Authors: B. Chetti, W. A. Crosby

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The work described in this paper is an investigation of the static and dynamic characteristics of two-lobe journal bearings taking into consideration the thermal effects. A thermo-hydrodynamic solution of a finite two-lobe journal bearing is performed by solving the generalized form Reynolds equation with the energy equation, taking into consideration viscosity variation across the film thickness. The static and dynamic characteristics were numerically obtained. The results are evaluated for different values of viscosity-temperature coefficient and Peclet number. The results show that considering the thermal effects in the solution of the two-lobe journal bearing has a marked on the study of its stability.

Keywords: two-lobe bearing, thermal effect, static, dynamic characteristics

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: A. Selmi

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Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.

Keywords: differential transformation method, functionally graded material, mode shape, natural frequency

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

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In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: asymptotics, continuous spectrum, difference equations, eigenvalues, jost functions, spectral singularities

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Authors: Reza Mohammadi, Mahdieh Sahebi

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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points

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Authors: Varun Joshi, Manish K. Rathod

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The latent heat thermal energy storage system is a thrust area of research due to exuberant thermal energy storage potential. The thermal performance of PCM is significantly augmented by installation of the high thermal conductivity fins. The objective of the present study is to obtain optimum size and location of the fins to enhance diffusion heat transfer without altering overall melting time. Hence, the constructal theory is employed to eliminate, resize, and re-position the fins. A numerical code based on conjugate heat transfer coupled enthalpy porosity approached is developed to solve Navier-Stoke and energy equation.The numerical results show that the constructal fin design has enhanced the thermal performance along with the increase in the overall volume of PCM when compared to conventional. The overall volume of PCM is found to be increased by half of total of volume of fins. The elimination and repositioning the fins at high temperature gradient from low temperature gradient is found to be vital.

Keywords: constructal theory, enthalpy porosity approach, phase change materials, fins

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Authors: R. Srinivas, K. V. Ramana

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This paper presents a novel method called VESTAL to label vertebrae and inter vertebral discs. Each vertebra has certain statistical features properties. To label vertebrae and discs, a new equation to model the path of spinal cord is derived using statistical properties of the spinal canal. VESTAL uses this equation for labeling vertebrae and discs. For each vertebrae and inter vertebral discs both posterior, interior width, height are measured. The calculated values are compared with real values which are measured using venires calipers and the comparison produced 95% efficiency and accurate results. The VESTAL is applied on 50 patients 350 MR images and obtained 100% accuracy in labeling.

Keywords: spine, vertebrae, inter vertebral disc, labeling, statistics, texture, disc

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Authors: M. Kiarna, S. Junjira, S. Casey, M. Nolwazi, M. S. Marcos, A. T. Tatiana, L. Cassandra

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This paper details a rebrand design project developed for a non-profitable organization called Te Roopu Waiora (TRW), which is currently located in Auckland, Aotearoa New Zealand. This social enterprise is dedicated to supporting the Māori community living with sensorial, physical and intellectual disabilities (whānau hauā). As part of a year three bachelor design brief, the rebrand project enabled students to reflect on Kaupapa Māori principles and appropriately address the values of the organisation. As such, the methodology used a pragmatic paradigm approach and mixed methods design practices involving a human-centred design to problem solving. As result, the student project culminated in the development in a range of cohesive design artefacts, aiming to improve the rentability and perception of the brand with the audience and stakeholders.

Keywords: design in Aotearoa New Zealand, Kaupapa Māori, branding, design education, human-centered design

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Authors: John P. Ulhøi

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Firms are faced with pressure to stay innovative and entrepreneurial while at the same time leaving lighter ecological footprints. Traditionally inspiration for new product development (NPD) has come from the creative in-house staff and from the marketplace. Often NPD offered by this approach has proven to be (far from) optimal for its purpose or highly (resource and energy) efficient. More recently, a bio-inspired NPD approach has surfaced under the banner of biomimetics. Biomimetics refers to inspiration from and translations of designs, systems, processes, and or specific properties that exist in nature. The principles and structures working in nature have evolved over a long period of time enable them to be optimized for the purpose and resource and energy-efficient. These characteristics reflect the raison d'être behind the field of biomimetics. While biological expertise is required to understand and explain such natural and biological principles and structures, engineers are needed to translate biological design and processes into synthetic applications. It can, therefore, hardly be surprising, biomimetics long has gained a solid foothold in both biology and engineering. The commercial adoption of biomimetic applications in new production development (NDP) in industry, however, does not quite reflect a similar growth. Differently put, this situation suggests that something is missing in the biomimetic-NPD-equation, thus acting as a brake towards the wider commercial application of biomimetics and thus the use of eco-materials and design in the industry. This paper closes some of that gap. Before concluding, avenues for future research and implications for practice will be briefly sketched out.

Keywords: biomimetics, eco-materials, NPD, commercialization

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Authors: Hao-Hsi Tseng, Hsin-Yun Lee

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In the process of building design, the designers have to complete the spatial design and consider the evacuation performance at the same time. It is usually difficult to combine the two planning processes and it results in the gap between spatial design and evacuation performance. Then the designers cannot complete an integrated optimal design solution. In addition, the evacuation routing models proposed by previous researchers is different from the practical evacuation decisions in the real field. On the other hand, more and more building design projects are executed by Building Information Modeling (BIM) in which the design content is formed by the object-oriented framework. Thus, the integration of BIM and evacuation simulation can make a significant contribution for designers. Therefore, this research plan will establish a model that integrates spatial design and evacuation planning. The proposed model will provide the support for the spatial design modifications and optimize the evacuation planning. The designers can complete the integrated design solution in BIM. Besides, this research plan improves the evacuation routing method to make the simulation results more practical. The proposed model will be applied in a building design project for evaluation and validation when it will provide the near-optimal design suggestion. By applying the proposed model, the integration and efficiency of the design process are improved and the evacuation plan is more useful. The quality of building spatial design will be better.

Keywords: building information modeling, evacuation, design, floor plan

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Authors: Nilanjana Chanda, Rangeet Bhattacharyya

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Grover’s search algorithm is the fastest possible quantum mechanical algorithm to search a certain element from an unstructured set of data of N items. The algorithm can determine the desired result in only O(√N) steps. It has been demonstrated theoretically and experimentally on two-qubit systems long ago. In this work, we investigate the fidelity of Grover’s search algorithm by implementing it on an open quantum system. In particular, we study with what accuracy one can estimate that the algorithm would deliver the searched state. In reality, every system has some influence on its environment. We include the environmental effects on the system dynamics by using a recently reported fluctuation-regulated quantum master equation (FRQME). We consider that the environment experiences thermal fluctuations, which leave its signature in the second-order term of the master equation through its appearance as a regulator. The FRQME indicates that in addition to the regular relaxation due to system-environment coupling, the applied drive also causes dissipation in the system dynamics. As a result, the fidelity is found to depend on both the drive-induced dissipative terms and the relaxation terms, and we find that there exists a competition between them, leading to an optimum drive amplitude for which the fidelity becomes maximum. For efficient implementation of the search algorithm, precise knowledge of this optimum drive amplitude is essential.

Keywords: dissipation, fidelity, quantum master equation, relaxation, system-environment coupling

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Authors: Jean-Marie Vilaire, Ricardo Abreu-Blaya, Juan Bory-Reyes

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The classical Beltrami system of elliptic equations generalizes the Cauchy Riemann equation in the complex plane and offers the possibility to consider homogeneous system with no terms of zero order. The theory of Douglis-valued functions, called Hyper-analytic functions, is special case of the above situation. In this note, we prove an analogue of the N. Davydov theorem in the framework of the theory of hyperanalytic functions. The used methodology contemplates characteristic methods of the hypercomplex analysis as well as the singular integral operators and elliptic systems of the partial differential equations theories.

Keywords: Beltrami equation, Douglis algebra-valued function, Hypercomplex Cauchy type integral, Sokhotski-Plemelj formulae

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Authors: Muslim Malik, Avadhesh Kumar

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A stronger concept of exact controllability which is called Total Controllability is introduced in this manuscript. Sufficient conditions have been established for the total controllability of a control problem, governed by second order nonlinear differential equation with delay and non-instantaneous impulses in a Banach space X. The results are obtained using the strongly continuous cosine family and Banach fixed point theorem. Also, the total controllability of an integrodifferential problem is investigated. At the end, some numerical examples are provided to illustrate the analytical findings.

Keywords: Banach fixed point theorem, non-instantaneous impulses, strongly continuous cosine family, total controllability

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Authors: Jihye Jeon

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This paper analyzes the conceptual framework of three statistical methods, multiple regression, path analysis, and structural equation models. When establishing research model of the statistical modeling of complex social phenomenon, it is important to know the strengths and limitations of three statistical models. This study explored the character, strength, and limitation of each modeling and suggested some strategies for accurate explaining or predicting the causal relationships among variables. Especially, on the studying of depression or mental health, the common mistakes of research modeling were discussed.

Keywords: multiple regression, path analysis, structural equation models, statistical modeling, social and psychological phenomenon

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Authors: Seyed Jamal Haddadi, M. Reza Mehranpour, Roya Sadat Mortazavi, Zahra Sadat Mortazavi

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Principal aim of this research is trajectory tracking, attitude and position control scheme in real flight mode by an Octorotor helicopter. For more stability, in this Unmanned Aerial Vehicle (UAV), number of motors is increased to eight motors which end of each arm installed two coaxial counter rotating motors. Dynamic model of this Octorotor includes of motion equation for translation and rotation. Utilized controller is proportional-integral-derivative (PID) control loop. The proposed controller is designed such that to be able to attenuate an effect of external wind disturbance and guarantee stability in this condition. The trajectory is determined by a Global Positioning System (GPS). Also an ARM CortexM4 is used as microprocessor. Electronic board of this UAV designed as able to records all of the sensors data, similar to an aircraft black box in external memory. Finally after auto landing of Octorotor, flight data is shown in MATLAB software and Experimental results of the proposed controller show the effectiveness of our approach on the Autonomous Quadrotor in real conditions.

Keywords: octorotor, design, PID controller, autonomous, trajectory tracking

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Authors: Tokuei Sako

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Laser-induced current in a quasi-one-dimensional nanostructure has been studied by a model of a few electrons confined in a 1D electrostatic potential coupled to electrodes at both ends and subjected to a pulsed laser field. The time-propagation of the one- and two-electron wave packets has been calculated by integrating the time-dependent Schrödinger equation directly by the symplectic integrator method with uniform Fourier grid. The temporal behavior of the resultant light-induced current in the studied systems has been discussed with respect to the lifetime of the quasi-bound states formed when the static bias voltage is applied.

Keywords: pulsed laser field, nanowire, electron wave packet, quantum dots, time-dependent Schrödinger equation

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Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan

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The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.

Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space

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Authors: Nan Hu, Wujun Wang

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In the ever-changing digital arena, augmented reality (AR) applications have transitioned from technological enthusiasm into business endeavors, signaling a near future in which AR applications are integrated into daily life. While practitioners in the design industry continue to explore AR’s potential for innovative communication, educators have taken steps to incorporate AR into the curricula for design, explore its creative potential, and realize early initiatives for teaching AR in design-related disciplines. In alignment with recent advancements, this paper presents a pedagogical model for a hybrid studio course in which students collaborate with AR alongside 3D modeling and graphic design. The course extended students’ digital capacity, fostered their design thinking skills, and immersed them in a multidisciplinary design process. This paper outlines the course and evaluates its effectiveness by discussing challenges encountered and outcomes generated in this particular pedagogical context. By sharing insights from the teaching experience, we aim to empower the community of design educators and offer institutions a valuable reference for advancing their curricular approaches. This paper is a testament to the ever-evolving landscape of design education and its response to the digital age.

Keywords: 3D, AR, augmented reality, design thinking, graphic design

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Authors: Hesham Shaalan

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Senior design projects teach students many important skills. One of the major goals is to prepare students to apply effective problem-solving techniques to a problem that represents a real-world situation. This includes the ability to define the problem, compare alternative solutions, identify the best solution, and design the system. This paper describes the design of a shipboard power plant as a senior project in the Marine Engineering program at the U.S. Merchant Marine Academy. The design project was supervised by faculty members who guided a multidisciplinary group of seniors. The research project was sponsored by the Office of Naval Research. Each group of seniors focused on one of the main design aspects of the project, including the electric power system, nuclear power plant, ship hull design, and economics.

Keywords: senior design project, shipboard power system, engineering education, marine engineering

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Authors: T. R. Sreeram, S. Natarajan, C. Jena

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Civil engineering construction is a network of tasks involving varying degree of complexity and streamlining, and standardization is the only way to establish a systemic approach to design. While there are off the shelf tools such as AutoCAD that play a role in the realization of design, the repeatable process in which these tools are deployed often is ignored. The present paper addresses this challenge through a sustainable design process and effective standardizations at all stages in the design workflow. The same is demonstrated through a case study in the context of construction, and further improvement points are highlighted.

Keywords: syste, lean, value stream, process improvement

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Authors: Ali Anwar, Hu Qinglei, Li Bo, Muhammad Taha Ali

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In this paper a generic model of perturbed nonlinear systems is considered which is affected by hard backlash nonlinearity at the input. The nonlinearity is modelled by a dynamic differential equation which presents a more precise shape as compared to the existing linear models and is compatible with nonlinear design technique such as backstepping. Moreover, a novel backstepping based nonlinear control law is designed which explicitly incorporates a continuous-time adaptive backlash inverse model. It provides a significant flexibility to control engineers, whereby they can use the estimated backlash spacing value specified on actuators such as gears etc. in the adaptive Backlash Inverse model during the control design. It ensures not only global stability but also stringent transient performance with desired precision. It is also robust to external disturbances upon which the bounds are taken as unknown and traverses the backlash spacing efficiently with underestimated information about the actual value. The continuous-time backlash inverse model is distinguished in the sense that other models are either discrete-time or involve complex computations. Furthermore, numerical simulations are presented which not only illustrate the effectiveness of proposed control law but also its comparison with PID and other backstepping controllers.

Keywords: adaptive control, hysteresis, backlash inverse, nonlinear system, robust control, backstepping

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Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

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Authors: Tarek Sabri Duzan

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Knowledge of the magnitude of Geo-pressures (Pore, Fracture & Over-burden pressures) is vital especially during drilling, completions, stimulations, Enhance Oil Recovery. Many times problems, like lost circulation could have been avoided if techniques for calculating Geo-pressures had been employed in the well planning, mud weight plan, and casing design. In this paper, we focused on the relationships between Geo-pressures and wave velocities (P-Wave (Vp) and S-wave (Vs)) in shallow Libyan carbonate reservoir in the western part of the Sirte Basin (Dahra F-Area). The data used in this report was collected from four new wells recently drilled. Those wells were scattered throughout the interested reservoir as shown in figure-1. The data used in this work are bulk density, Formation Mult -Tester (FMT) results and Acoustic wave velocities. Furthermore, Eaton Method is the most common equation used in the world, therefore this equation has been used to calculate Fracture pressure for all wells using dynamic Poisson ratio calculated by using acoustic wave velocities, FMT results for pore pressure, Overburden pressure estimated by using bulk density. Upon data analysis, it has been found that there is a linear relationship between Geo-pressures (Pore, Fracture & Over-Burden pressures) and wave velocities ratio (Vp/Vs). However, the relationship was not clear in the high-pressure area, as shown in figure-10. Therefore, it is recommended to use the output relationship utilizing the new seismic data for shallow carbonate reservoir to predict the Geo-pressures for future oil operations. More data can be collected from the high-pressure zone to investigate more about this area.

Keywords: bulk density, formation mult-tester (FMT) results, acoustic wave, carbonate shalow reservoir, d/jfield velocities

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Authors: Mogens Saberi

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This paper presents different design approaches for the design of turbine foundations. In the design process, several unknown factors must be considered such as the soil stiffness at the site. The main static and dynamic loads are presented and the results of a dynamic simulation are presented for a turbine foundation that is currently being built. A turbine foundation is an important part of a power plant since a non-optimal behavior of the foundation can damage the turbine itself and thereby stop the power production with large consequences.

Keywords: dynamic turbine design, harmonic response analysis, practical turbine design experience, concrete foundation

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Authors: Adrian Priceputu, Elena Mihaela Stan

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Our research addresses a critical challenge in renewable energy: improving efficiency and reducing the costs associated with the installation of ground-mounted photovoltaic (PV) panels. The most commonly used foundation solution is metal piles - with various sections adapted to soil conditions and the structural model of the panels. However, direct foundation systems are also sometimes used, especially in brownfield sites. Although metal micropiles are generally the first design option, understanding and predicting their bearing capacity, particularly under varied soil conditions, remains an open research topic. CPT Method and Current Challenges: Metal piles are favored for PV panel foundations due to their adaptability, but existing design methods rely heavily on costly and time-consuming in situ tests. The Cone Penetration Test (CPT) offers a more efficient alternative by providing valuable data on soil strength, stratification, and other key characteristics with reduced resources. During the test, a cone-shaped probe is pushed into the ground at a constant rate. Sensors within the probe measure the resistance of the soil to penetration, divided into cone penetration resistance and shaft friction resistance. Despite some existing CPT-based design approaches for metal piles, these methods are often cumbersome and difficult to apply. They vary significantly due to soil type and foundation method, and traditional approaches like the LCPC method involve complex calculations and extensive empirical data. The method was developed by testing 197 piles on a wide range of ground conditions, but the tested piles were very different from the ones used for PV pile foundations, making the method less accurate and practical for steel micropiles. Project Objectives and Methodology: Our research aims to develop a calculation method for metal micropile foundations using CPT data, simplifying the complex relationships involved. The goal is to estimate the pullout bearing capacity of piles without additional laboratory tests, streamlining the design process. To achieve this, a case study was selected which will serve for the development of an 80ha solar power station. Four testing locations were chosen spread throughout the site. At each location, two types of steel profiles (H160 and C100) were embedded into the ground at various depths (1.5m and 2.0m). The piles were tested for pullout capacity under natural and inundated soil conditions. CPT tests conducted nearby served as calibration points. The results served for the development of a preliminary equation for estimating pullout capacity. Future Work: The next phase involves validating and refining the proposed equation on additional sites by comparing CPT-based forecasts with in situ pullout tests. This validation will enhance the accuracy and reliability of the method, potentially transforming the foundation design process for PV panels.

Keywords: cone penetration test, foundation optimization, solar power stations, steel pile foundations

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Authors: Ralpian Randolian

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Eighty-five Romanian teachers and principals participated on this study to examine their perspectives of different leadership styles. Demographic variables such as the source of degree (Romania, Europe institutes, USA institutes, etc.), gender, region, level taught, years of experience, and specialty were identified. The researcher developed a questionnaire that consisted of 4 leadership styles. The data were analyzed using structural equation modeling (SEM) to identify which of the variables best predict the leadership styles. Results indicated that the democracy style was the most preferred leadership style by Jordanian parents, while the authoritarian styles ranked second. The results also found statistically significant differences were found related to the study variables. This study ends by putting forward a number of suggestions and recommendation.

Keywords: teachers’ perspectives, leadership styles, gender, structural equation modeling

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Authors: Beghdadi Lotfi, Bouziane Abdelhafid

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A finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation. In this scheme, based on the integration around the polygonal control volume, the derivatives of conduction equation must be converted into closed line integrals using same formulation of the Stokes theorem. To valid the accuracy of the method two numerical experiments s are used: conduction in a regular block (with known analytical solution) and conduction in a rotated block (case with curved boundaries).The numerical results show good agreement with analytical results. To demonstrate the accuracy of the method, the absolute and root-mean square errors versus the grid size are examined quantitatively.

Keywords: Stokes theorem, unstructured grid, heat transfer, complex geometry

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Authors: Xu Runzhang, Yang Yanbing, Niu Yi, Zhang Mingyou, Liu Yu

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For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(Ω). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level.

Keywords: high energy level, critical energy level, linear dynamical boundary condition, semilinear parabolic equation

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