A Generalization of Prefactored Compact Schemes for Advection Equations
For researchers in computational fluid dynamics, this provides a more efficient method for solving advection equations, though it is incremental as it extends existing prefactorization ideas.
The paper proposes a generalized prefactorization of compact schemes for advection equations that reduces computational load by avoiding inversion of multi-diagonal matrices while preserving accuracy up to 16th order. Test cases show preserved accuracy and increased computational efficiency.
A generalized prefactorization of compact schemes aimed at reducing the stencil and improving the computational efficiency is proposed here in the framework of transport equations. By the prefactorization introduced here, the computational load associated with inverting multi-diagonal matrices is avoided, while the order of accuracy is preserved. The prefactorization can be applied to any centered compact difference scheme with arbitrary order of accuracy (results for compact schemes of up to sixteenth order of accuracy are included in the study). One notable restriction is that the proposed schemes can be applied in a predictor-corrector type marching scheme framework. Two test cases, associated with linear and nonlinear advection equations, respectively, are included to show the preservation of the order of accuracy and the increase of the computational efficiency of the prefactored compact schemes.