Search results for: Numerical inversion

Authors: Kazuhisa Koda, Tsutomu Kobayashi

Abstract:

Laura Island, which is located about 50 km away from downtown, is a source of water supply in Majuro atoll, which is the capital of the Republic of the Marshall Islands. Low and flat Majuro atoll has neither river nor lake. It is very important for Majuro atoll to ensure the conservation of its water resources. However, upconing, which is the process of partial rising of the freshwater-saltwater boundary near the water-supply well, was caused by the excess pumping from it during the severe drought in 1998. Upconing will make the water usage of the freshwater lens difficult. Thus, appropriate water usage is required to prevent up coning in the freshwater lens because there is no other water source during drought. Numerical simulation of water usage applying SEAWAT model was conducted at the central part of Laura Island, including the water supply well, which was affected by upconing. The freshwater lens was created as a result of infiltration of consistent average rainfall. The lens shape was almost the same as the one in 1985. 0 of monthly rainfall and variable daily pump discharge were used to calculate the sustainable pump discharge from the water supply well. Consequently, the total amount of pump discharge was increased as the daily pump discharge was increased, indicating that it needs more time to recover from upconing. Thus, a pump standard to reduce the pump intensity is being proposed, which is based on numerical simulation concerning the occurrence of the up-coning phenomenon in Laura Island during the drought.

Keywords: Freshwater lens, islands, numerical simulation, sustainable water use.

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Authors: M. Mahdi, N. Shariatmadari

Abstract:

Since, both the relative position of tunnels and the construction procedure affect the soil movement and internal forces in the lining, it is of major concern to study the influence of these factors on the tunnel design. Construction procedures of tunnels have considerable effects on the magnitude of surface movements and lining stresses. This paper describes numerical analysis of construction procedure of a three adjacent shallow tunnels at high groundwater levels using the commercial finite difference software (FLAC-3D). The aim of this study is to determinate the most suitable construction procedure for the three tunnels and the optimum excavation step in Tehran Metro tunnels in order to optimize the surface settlements and lining stresses.

Keywords: Shallow tunnel, multiple tunnels, construction procedure, surface movement, numerical modeling.

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Authors: Buntara Sthenly Gan

Abstract:

A novel and versatile numerical technique to solve a self-stress equilibrium state is adopted herein as a form-finding procedure for an irregular tensegrity structure. The numerical form-finding scheme of a tensegrity structure uses only the connectivity matrix and prototype tension coefficient vector as the initial guess solution. Any information on the symmetrical geometry or other predefined initial structural conditions is not necessary to get the solution in the form-finding process. An eight-node initial condition example is presented to demonstrate the efficiency and robustness of the proposed method in the form-finding of an irregular tensegrity structure. Based on the conception from the form-finding of an eight-node irregular tensegrity structure, a monumental object is designed by considering the real world situation such as self-weight, wind and earthquake loadings.

Keywords: Tensegrity, Form-finding, Design, Irregular, Self-stress, Force density method.

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Authors: M.Imanova, G.Mehdiyeva, V.Ibrahimov

Abstract:

Solution of some practical problems is reduced to the solution of the integro-differential equations. But for the numerical solution of such equations basically quadrature methods or its combination with multistep or one-step methods are used. The quadrature methods basically is applied to calculation of the integral participating in right hand side of integro-differential equations. As this integral is of Volterra type, it is obvious that at replacement with its integrated sum the upper limit of the sum depends on a current point in which values of the integral are defined. Thus we receive the integrated sum with variable boundary, to work with is hardly. Therefore multistep method with the constant coefficients, which is free from noted lack and gives the way for finding it-s coefficients is present.

Keywords: Volterra integro-differential equations, multistepmethods, finite-difference methods, initial value problem

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Authors: M. Amoura, M. Alloti, A. Mouassi, N. Zeraibi

Abstract:

Heat transfer behavior of three different types of nanofluids flowing through a horizontal tube under laminar regime has been investigated numerically. The wall of tube is maintained at constant temperature. Al₂O₃-water, CuO-water and TiO₂-water are used with different Reynolds number and different volume fraction. The numerical results of heat transfer indicate that the Nusselt number of nanofluids is larger than that of the base fluid. The Pressure loss coefficient decreases by increasing Reynolds number for all types of nanofluids. Results of Nusselt number enhancement and pressure loss coefficient enhancement indicate that Al₂O₃ nanoparticules give the best results in term of thermal-hydrolic properties.

Keywords: Heat transfer, Laminar flow, Nanofluid, Numerical study.

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Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

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, stability analysis.

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Authors: G.Mehdiyeva, V.Ibrahimov, M.Imanova

Abstract:

As is known, one of the priority directions of research works of natural sciences is introduction of applied section of contemporary mathematics as approximate and numerical methods to solving integral equation into practice. We fare with the solving of integral equation while studying many phenomena of nature to whose numerically solving by the methods of quadrature are mainly applied. Taking into account some deficiency of methods of quadrature for finding the solution of integral equation some sciences suggested of the multistep methods with constant coefficients. Unlike these papers, here we consider application of hybrid methods to the numerical solution of Volterra integral equation. The efficiency of the suggested method is proved and a concrete method with accuracy order p = 4 is constructed. This method in more precise than the corresponding known methods.

Keywords: Volterra integral equation, hybrid methods, stability and degree, methods of quadrature

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Authors: S. Bennoud, M. Zergoug

Abstract:

The numerical simulation of electromagnetic interactions is still a challenging problem, especially in problems that result in fully three dimensional mathematical models.

The goal of this work is to use mathematical modeling to characterize the reliability and capacity of eddy current technique to detect and characterize defects embedded in aeronautical in-service pieces.

The finite element method is used for describing the eddy current technique in a mathematical model by the prediction of the eddy current interaction with defects. However, this model is an approximation of the full Maxwell equations.

In this study, the analysis of the problem is based on a three dimensional finite element model that computes directly the electromagnetic field distortions due to defects.

Keywords: Eddy current, Finite element method, Non destructive testing, Numerical simulations.

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Authors: Arturo Ayala-Hernandez, Humberto H´ıjar

Abstract:

We propose a new alternative method for imposing fluid-solid boundary conditions in simulations of Multiparticle Collision Dynamics. Our method is based on the introduction of an explicit potential force acting between the fluid particles and a surface representing a solid boundary. We show that our method can be used in simulations of plane Poiseuille flows. Important quantities characterizing the flow and the fluid-solid interaction like the slip coefficient at the solid boundary and the effective viscosity of the fluid, are measured in terms of the set of independent parameters defining the numerical implementation. We find that our method can be used to simulate the correct hydrodynamic flow within a wide range of values of these parameters.

Keywords: Multiparticle Collision Dynamics, Fluid-Solid Boundary Conditions, Molecular Dynamics.

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Authors: Hassan A. Alshahrani, Mehdi H. Hojjati

Abstract:

In order to predict and model wrinkling which is caused by out of plane deformation due to compressive loading in the plane of the material during composite prepregs forming, it is necessary to quantitatively understand the relative magnitude of the bending stiffness. This study aims to examine the bending properties of out-of-autoclave (OOA) thermosetting prepreg under vertical cantilever test condition. A direct method for characterizing the bending behavior of composite prepregs was developed. The results from direct measurement were compared with results derived from an image-processing procedure that analyses the captured image during the vertical bending test. A numerical simulation was performed using ABAQUS to confirm the bending stiffness value.

Keywords: Bending stiffness, out of autoclave prepreg, forming process, numerical simulation.

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Authors: T. Benmiloud, A. Omari

Abstract:

This paper presents a new technique of compensation of the effect of variation parameters in the direct field oriented control of induction motor. The proposed method uses an adaptive tuning of the value of synchronous speed to obtain the robustness for the field oriented control. We show that this adaptive tuning allows having robustness for direct field oriented control to changes in rotor resistance, load torque and rotational speed. The effectiveness of the proposed control scheme is verified by numerical simulations. The numerical validation results of the proposed scheme have presented good performances compared to the usual direct-field oriented control.

Keywords: Induction motor, direct field-oriented control, compensation of variation parameters, fuzzy logic controller.

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Authors: Fuziyah Ishak, Mohamed B. Suleiman, Zanariah A. Majid, Khairil I. Othman

Abstract:

This paper considers the development of a two-point predictor-corrector block method for solving delay differential equations. The formulae are represented in divided difference form and the algorithm is implemented in variable stepsize variable order technique. The block method produces two new values at a single integration step. Numerical results are compared with existing methods and it is evident that the block method performs very well. Stability regions of the block method are also investigated.

Keywords: block method, delay differential equations, predictor-corrector, stability region, variable stepsize variable order.

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Authors: Ho Phu TRAN, Frédéric PLOURDE

Abstract:

The ongoing effort to develop an in-house compressible solver with multi-disciplinary physics is presented in this paper. Basic compressible solver combined with IBM technique provides us an effective numerical tool able to tackle the physics phenomena and especially physic phenomena involved in Solid Rocket Motors (SRMs). Main principles are introduced step by step describing its implementation. This paper sheds light on the whole potentiality of our proposed numerical model and we strongly believe a way to introduce multi-physics mechanisms strongly coupled is opened to ablation in nozzle, fluid/structure interaction and burning propellant surface with time.

Keywords: Compressible Flow, Immersed Boundary Method, Multi-disciplinary physics, Solid Rocket Motors.

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Authors: Heval Serhat Uluk, Sam M. Dakka, Kuldeep Singh, Richard Jefferson-Loveday

Abstract:

This paper will focus on the suitability of a trapped vortex combustor as a candidate for gas turbine combustor objectives to minimize pressure drop across the combustor and investigate aerodynamic performance. Non-reacting simulation of axisymmetric cavity trapped vortex combustors was run to investigate the pressure drop for various cavity aspect ratios of 0.3, 0.6 and 1 and for air mass flow rates of 14 m/s, 28 m/s and 42 m/s. A numerical study of an axisymmetric trapped vortex combustor was carried out by using two-dimensional and three-dimensional computational domains. A comparison study was conducted between Reynolds Averaged Navier Stokes (RANS) k-ε Realizable with enhanced wall treatment and RANS k-ω Shear Stress Transport (SST) models to find the most suitable turbulence model. It was found that the k-ω SST model gives relatively close results to experimental outcomes. The numerical results were validated and showed good agreement with the experimental data. Pressure drop rises with increasing air mass flow rate, and the lowest pressure drop was observed at 0.6 cavity aspect ratio for all air mass flow rates tested, which agrees with the experimental outcome. A mixing enhancement study showed that 30-degree angle air injectors provide improved fuel-air mixing.

Keywords: Aerodynamic, Computational Fluid Dynamics, Propulsion, Trapped Vortex Combustor.

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Authors: Geeta Partap, Nitika Chugh

Abstract:

The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler-Bernoulli beam resonators, due to Exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection.The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for Deflection of beam under Simply Supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.

Keywords: Microstretch, deflection, exponential load, Laplace transforms, Residue theorem, simply supported.

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Authors: N. Kh. Gomidze, I. N. Jabnidze, K. A. Makharadze

Abstract:

The influence of inhomogeneities of plasma and statistical characteristics on the propagation of signal is very actual in wireless communication systems. While propagating in the media, the deformation and evaluation of the signal in time and space take place and on the receiver we get a deformed signal. The present article is dedicated to studying the space-time evolution of rectangular, sinusoidal, exponential and bi-exponential impulses via numerical experiment in the collisional, cold plasma. The presented method is not based on the Fourier-presentation of the signal. Analytically, we have received the general image depicting the space-time evolution of the radio impulse amplitude that gives an opportunity to analyze the concrete results in the case of primary impulse.

Keywords: Collisional, cold plasma, rectangular pulse signal, impulse envelope.

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Authors: Shinji Kajiwara

Abstract:

The spring-driven ball-type check valve is one of the most important components of hydraulic systems: it controls the position of the ball and prevents backward flow. To simplify the structure, the spring must be eliminated, and to accomplish this, the flow pattern and the behavior of the check ball in L-shaped pipe must be determined. In this paper, we present a full-scale model of a check ball made of acrylic resin, and we determine the relationship between the initial position of the ball, the position and diameter of the inflow port. The check flow rate increases in a standard center inflow model, and it is possible to greatly decrease the check-flow rate by shifting the inflow from the center.

Keywords: Hydraulics, Pipe Flow, Numerical Simulation, Flow Visualization, Check ball, L-shaped Pipe.

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Authors: Morteza Khaleghi Meybodi, Hossein Bisadi

Abstract:

Explosive forming is one of the unconventional techniques in which, most commonly, the water is used as the pressure transmission medium. One of the newest methods in explosive forming is gas detonation forming which uses a normal shock wave derived of gas detonation, to form sheet metals. For this purpose a detonation is developed from the reaction of H2+O2 mixture in a long cylindrical detonation tube. The detonation wave goes through the detonation tube and acts as a blast load on the steel blank and forms it. Experimental results are compared with a finite element model; and the comparison of the experimental and numerical results obtained from strain, thickness variation and deformed geometry is carried out. Numerical and experimental results showed approximately 75 – 90 % similarity in formability of desired shape. Also optimum percent of gas mixture obtained when we mix 68% H2 with 32% O2.

Keywords: Explosive forming, High strain rate, Gas detonation, Finite element analysis.

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Authors: Marco Raciti Castelli, Paolo Cioppa, Ernesto Benini

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This paper presents a CFD analysis of the flow field around a thin flat plate of infinite span inclined at 90° to a fluid stream of infinite extent. Numerical predictions have been compared to experimental measurements, in order to assess the potential of the finite volume code of determining the aerodynamic forces acting on a bluff body invested by a fluid stream of infinite extent. Several turbulence models and spatial node distributions have been tested. Flow field characteristics in the neighborhood of the flat plate have been investigated, allowing the development of a preliminary procedure to be used as guidance in selecting the appropriate grid configuration and the corresponding turbulence model for the prediction of the flow field over a two-dimensional vertical flat plate.

Keywords: CFD, vertical flat plate, aerodynamic force

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Authors: Juhee Lee, Yongjun Lee

Abstract:

In designing a low-energy-consuming buildings, the heat transfer through a large glass or wall becomes critical. Multiple layers of the window glasses and walls are employed for the high insulation. The gravity driven air flow between window glasses or wall layers is a natural heat convection phenomenon being a key of the heat transfer. For the first step of the natural heat transfer analysis, in this study the development and application of a finite volume method for the numerical computation of viscous incompressible flows is presented. It will become a part of the natural convection analysis with high-order scheme, multi-grid method, and dual-time step in the future. A finite volume method based on a fully-implicit second-order is used to discretize and solve the fluid flow on unstructured grids composed of arbitrary-shaped cells. The integrations of the governing equation are discretised in the finite volume manner using a collocated arrangement of variables. The convergence of the SIMPLE segregated algorithm for the solution of the coupled nonlinear algebraic equations is accelerated by using a sparse matrix solver such as BiCGSTAB. The method used in the present study is verified by applying it to some flows for which either the numerical solution is known or the solution can be obtained using another numerical technique available in the other researches. The accuracy of the method is assessed through the grid refinement.

Keywords: Finite volume method, fluid flow, laminar flow, unstructured grid.

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Authors: Rakesh Arasu, Sasitharan Ambicapathy, Sivaraj Ponnusamy, Mohanraj Murugesan, V. R. Sanal Kumar

Abstract:

The flow field within the combustor of scramjet engine is very complex and poses a considerable challenge in the design and development of a supersonic combustor with an optimized geometry. In this paper comprehensive numerical studies on flow field characteristics of different cavity based scramjet combustors with transverse injection of hydrogen have been carried out for both non-reacting and reacting flows. The numerical studies have been carried out using a validated 2D unsteady, density based 1st-order implicit k-omega turbulence model with multi-component finite rate reacting species. The results show a wide variety of flow features resulting from the interactions between the injector flows, shock waves, boundary layers, and cavity flows. We conjectured that an optimized cavity is a good choice to stabilize the flame in the hypersonic flow, and it generates a recirculation zone in the scramjet combustor. We comprehended that the cavity based scramjet combustors having a bearing on the source of disturbance for the transverse jet oscillation, fuel/air mixing enhancement, and flameholding improvement. We concluded that cavity shape with backward facing step and 45o forward ramp is a good choice to get higher temperatures at the exit compared to other four models of scramjet combustors considered in this study.

Keywords: Flame holding, Hypersonic flow, Scramjet combustor, Supersonic combustor.

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Authors: Baseem Khan, Ganga Agnihotri

Abstract:

Restructuring of Electricity supply industry introduced many issues such as transmission pricing, transmission loss allocation and congestion management. Many methodologies and algorithms were proposed for addressing these issues. In this paper a power flow tracing based method is proposed which involves Matrices methodology for the transmission usage and loss allocation for generators and demands. This method provides loss allocation in a direct way because all the computation is previously done for usage allocation. The proposed method is simple and easy to implement in a large power system. Further it is less computational because it requires matrix inversion only a single time. After usage and loss allocation cooperative game theory is applied to results for finding efficient economic signals. Nucleolus and Shapely value approach is used for optimal allocation of results. Results are shown for the IEEE 6 bus system and IEEE 14 bus system.

Keywords: Modified Kirchhoff Matrix, Power flow tracing, Transmission Pricing, Transmission Loss Allocation.

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Authors: Yiqin Lin, Liang Bao, Yimin Wei

Abstract:

In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.

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Authors: M. Behbahani-Nejad, Y. Shekari

Abstract:

A reduced order modeling approach for natural gas transient flow in pipelines is presented. The Euler equations are considered as the governing equations and solved numerically using the implicit Steger-Warming flux vector splitting method. Next, the linearized form of the equations is derived and the corresponding eigensystem is obtained. Then, a few dominant flow eigenmodes are used to construct an efficient reduced-order model. A well-known test case is presented to demonstrate the accuracy and the computational efficiency of the proposed method. The results obtained are in good agreement with those of the direct numerical method and field data. Moreover, it is shown that the present reduced-order model is more efficient than the conventional numerical techniques for transient flow analysis of natural gas in pipelines.

Keywords: Eigenmode, Natural Gas, Reduced Order Modeling, Transient Flow.

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Authors: V. Salajka, J. Kala, P. Hradil

Abstract:

The presented article deals with the description of a numerical model of a corridor at a Central Interim Spent Fuel Storage Facility (hereinafter CISFSF). The model takes into account the effect of air flows on the temperature of stored waste. The computational model was implemented in the ANSYS/CFX programming environment in the form of a CFD task solution, which was compared with an approximate analytical calculation. The article includes a categorization of the individual alternatives for the ventilation of such underground systems. The aim was to evaluate a ventilation system for a CISFSF with regard to its stability and capacity to provide sufficient ventilation for the removal of heat produced by stored casks with spent nuclear fuel.

Keywords: Temperature fields, Spent Fuel, Interim storage facility, CFD.

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Authors: Samira Laidaoui, Mohammed Djermane, Nazihe Terfaya

Abstract:

The fluid-structure coupling is a natural phenomenon which reflects the effects of two continuums: fluid and structure of different types in the reciprocal action on each other, involving knowledge of elasticity and fluid mechanics. The solution for such problems is based on the relations of continuum mechanics and is mostly solved with numerical methods. It is a computational challenge to solve such problems because of the complex geometries, intricate physics of fluids, and complicated fluid-structure interactions. The way in which the interaction between fluid and solid is described gives the largest opportunity for reducing the computational effort. In this paper, a problem of fluid structure interaction is investigated with two-way coupling method. The formulation Arbitrary Lagrangian-Eulerian (ALE) was used, by considering a dynamic grid, where the solid is described by a Lagrangian formulation and the fluid by a Eulerian formulation. The simulation was made on the ANSYS software.

Keywords: ALE, coupling, FEM, fluid-structure interaction, one-way method, two-way method.

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Authors: Takashi Ueda, Shinichi Enoki

Abstract:

Forging parts is used to automobiles; because, they have high strength and it is possible to press them into complicated shape. When itis possible to manufacture hollow forging parts, it leads to reduce weightof the automobiles. But, hollow forging parts are confined to axisymmetrical shape. Hollowforging parts that were pressed to complicated shape are expected. Therefore, we forge a blank that aluminum alloy was inserted in stainless steel. After that, we can providecomplex forging parts that are reduced weight,ifit is possible to be melted the aluminum alloy away by using different of melting points.It is necessary to establish heat forging analysis methodon blank consist of stainless steel and aluminum alloy. Because,this forging is different from conventional forging and this technology is not confirmed. In this study, we compared forging experiment with numerical analysis on the view point of forming load and shape after forming and establish how to set the material temperaturesof two metals and material property of stainless steel on the analysis method. Consequently, temperature difference of stainless steel and aluminum alloy was obtained by experiment. We got material property of stainless steel on forging experimental by compression tests. We had compared numerical analysis that was used the temperature difference of two metals and the material property of stainless steel on forging experimental with forging experiment. Forging analysis method on blankconsist of two metals was established by result of numerical analysis having agreedwith result of forging experiment.

Keywords: Forging, lightweight, analysis, hollow.

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Authors: Ashwani K. Rana, Narottam Chand, Vinod Kapoor

Abstract:

In this paper, gate leakage current has been mitigated by the use of novel nanoscale MOSFET with Source/Drain-to-Gate Non-overlapped and high-k spacer structure for the first time. A compact analytical model has been developed to study the gate leakage behaviour of proposed MOSFET structure. The result obtained has found good agreement with the Sentaurus Simulation. Fringing gate electric field through the dielectric spacer induces inversion layer in the non-overlap region to act as extended S/D region. It is found that optimal Source/Drain-to-Gate Non-overlapped and high-k spacer structure has reduced the gate leakage current to great extent as compared to those of an overlapped structure. Further, the proposed structure had improved off current, subthreshold slope and DIBL characteristic. It is concluded that this structure solves the problem of high leakage current without introducing the extra series resistance.

Keywords: Gate tunneling current, analytical model, spacer dielectrics, DIBL, subthreshold slope.

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Authors: Weihao Chung, Iau-Teh Wang, Yu-Hsi Hu

Abstract:

This is the second part of the paper. It, aside from the core subroutine test reported previously, focuses on the simulation of turbulence governed by the full STF Navier-Stokes equations on a large scale. Law of the wall is found plausible in this study as a model of the boundary layer dynamics. Model validations proceed to include velocity profiles of a stationary turbulent Couette flow, pure sloshing flow simulations, and the identification of water-surface inclination due to fluid accelerations. Errors resulting from the irrotational and hydrostatic assumptions are explored when studying a wind-driven water circulation with no shakings. Illustrative examples show that this numerical strategy works for the simulation of sloshing-shear mixed flow in a 3-D rigid rectangular base tank.

Keywords: potential flow theory, sloshing flow, space-timefiltering, order of accuracy.

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Authors: R. Faiez, M. Mashhoudi, F. Najafi

Abstract:

Implicit in most large-scale numerical analyses of the crystal growth from the melt is the assumption that the shape and position of the phase boundary are determined by the transport phenomena coupled strongly to the melt hydrodynamics. In the present numerical study, the interface shape-effect on the convective interactions in a Czochralski oxide melt is described. It was demonstrated that thermocapillary flow affects inversely the phase boundaries of distinct shapes. The inhomogenity of heat flux and the location of the stagnation point at the crystallization front were investigated. The forced convection effect on the point displacement at the boundary found to be much stronger for the flat plate interface compared to the cone-shaped one with and without the Marangoni flow.

Keywords: Computer simulation, fluid flow, interface shape, thermocapillary effect.

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