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A 15-point high-order compact scheme with multigrid computation for solving 3D convection diffusion equations |
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| Authors: | Yin Wang Su Yu Ruxin Dai Jun Zhang |
| Affiliation: | 1. Department of Mathematics and Computer Science, Lawrence Technological University, Southfield, MI 48075, USA;2. College of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China;3. Department of Computer Science, Laboratory for High Performance Scientific Computing and Computer Simulation, University of Kentucky, Lexington, KY 40506-0046, USA |
| Abstract: | We propose a method with sixth-order accuracy to solve the three-dimensional (3D) convection diffusion equation. We first use a 15-point fourth-order compact discretization scheme to obtain fourth-order solutions on both fine and coarse grids using the multigrid method. Then an iterative mesh refinement technique combined with Richardson extrapolation is used to approximate the sixth-order accurate solution on the fine grid. Numerical results are presented for a variety of test cases to demonstrate the efficiency and accuracy of the proposed method, compared with the standard fourth-order compact scheme. |
| Keywords: | convection diffusion equation 15-point stencil Reynolds number multigrid method sixth-order compact scheme |