Operator-splitting Methods Respecting Eigenvalue Problems for Convection-diffusion and Wave Equations
نویسنده
چکیده
We discuss iterative operator-splitting methods for convection-diffusion and wave equations motivated from the eigenvalue problem to decide the splitting process. The operator-splitting methods are well-know to solve such complicated multi-dimensional and multi-physical problems. Often the problem, how to decouple the underlying operators, is not understood well enough. We propose a method based on computing the eigenvalues for the simpler problem to decide the splitting operators and the time steps. We present the analysis and the numerical results.
منابع مشابه
Operator-splitting methods in respect of eigenvalue problems for nonlinear equations and applications for Burgers equations
In this article we consider iterative operator-splitting methods for nonlinear differential equations with respect to their eigenvalues. The main feature of the proposed idea is the fixed-point iterative scheme that linearizes our underlying equations. Based on the approximated eigenvalues of such linearized systems we choose the order of the the operators for our iterative splitting scheme. Th...
متن کاملFast explicit operator splitting method for convection-diffusion equations
Systems of convection–diffusion equations model a variety of physical phenomena which often occur in real life. Computing the solutions of these systems, especially in the convection dominated case, is an important and challenging problem that requires development of fast, reliable and accurate numerical methods. In this paper, we propose a second-order fast explicit operator splitting (FEOS) m...
متن کاملAdditive Operator Splitting Methods for Solving Systems of Nonlinear Finite Difference Equations
There exists a considerably body of literature on the development, analysis and implementation of multiplicative and additive operator splitting methods for solving large and sparse systems of finite difference equations arising from the discretization of partial differential equations. In this note, we will review the Newton–Arithmetic Mean and the Modified Newton–Arithmetic Mean methods for s...
متن کاملA Modified Flux Vector Splitting Scheme for Flow Analysis in Shock Wave Laminar Boundary Layer Interactions
The present work introduces a modified scheme for the solution of compressible 2-D full Navier-Stokes equations, using Flux Vector Splitting method. As a result of this modification, numerical diffusion is reduced. The computer code which is developed based on this algorithm can be used easily and accurately to analyze complex flow fields with discontinuity in properties, in cases such as shock...
متن کاملA Modified Flux Vector Splitting Scheme for Flow Analysis in Shock Wave Laminar Boundary Layer Interactions
The present work introduces a modified scheme for the solution of compressible 2-D full Navier-Stokes equations, using Flux Vector Splitting method. As a result of this modification, numerical diffusion is reduced. The computer code which is developed based on this algorithm can be used easily and accurately to analyze complex flow fields with discontinuity in properties, in cases such as shock...
متن کامل