High-order compact LOD methods for solving high-dimensional advection equations

Abstract In this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for third derivatives in truncation error remainder, two high-order compact LOD schemes are established solving two- three- dimensional advection equations, respectively. They have fourth-order accuracy both time space. By von Neumann analysis it shows that unconditionally stable. Besides, consistency convergence of them also proved. Finally, numerical experiments given to confirm efficiency present schemes.