{"title":"The Splitting Upwind Schemes for Spectral Action Balance Equation","authors":"Anirut Luadsong, Nitima Aschariyaphotha","country":null,"institution":"","volume":54,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":899,"pagesEnd":908,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/12679","abstract":"The spectral action balance equation is an equation that\r\nused to simulate short-crested wind-generated waves in shallow water\r\nareas such as coastal regions and inland waters. This equation consists\r\nof two spatial dimensions, wave direction, and wave frequency which\r\ncan be solved by finite difference method. When this equation with\r\ndominating convection term are discretized using central differences,\r\nstability problems occur when the grid spacing is chosen too coarse.\r\nIn this paper, we introduce the splitting upwind schemes for avoiding\r\nstability problems and prove that it is consistent to the upwind scheme\r\nwith same accuracy. The splitting upwind schemes was adopted\r\nto split the wave spectral action balance equation into four onedimensional\r\nproblems, which for each small problem obtains the\r\nindependently tridiagonal linear systems. For each smaller system\r\ncan be solved by direct or iterative methods at the same time which\r\nis very fast when performed by a multi-processor computer.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 54, 2011"}