High-order compact LOD methods for solving high-dimensional advection equations. (English) Zbl 1476.35136
Summary: In this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for the third derivatives in the truncation error remainder, two high-order compact LOD schemes are established for solving the two- and three- dimensional advection equations, respectively. They have the fourth-order accuracy in both time and space. By the von Neumann analysis method, it shows that the two schemes are unconditionally stable. Besides, the consistency and convergence of them are also proved. Finally, numerical experiments are given to confirm the accuracy and efficiency of the present schemes.
MSC:
| 35L35 | Initial-boundary value problems for higher-order hyperbolic equations |
| 35G16 | Initial-boundary value problems for linear higher-order PDEs |
Keywords:
advection equation; high-order compact difference scheme; LOD method; stability and convergenceReferences:
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