The Semi-implicit DLN Algorithm for the Navier Stokes Equations

Autor:	Pei, Wenlong
Rok vydání:	2023
Předmět:	Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	Dahlquist, Liniger, and Nevanlinna design a family of one-leg, two-step methods (the DLN method) that is second order, A- and G-stable for arbitrary, non-uniform time steps. Recently, the implementation of the DLN method can be simplified by the refactorization process (adding time filters on backward Euler scheme). Due to these fine properties, the DLN method has strong potential for the numerical simulation of time-dependent fluid models. In the report, we propose a semi-implicit DLN algorithm for the Navier Stokes equations (avoiding non-linear solver at each time step) and prove the unconditional, long-term stability and second-order convergence with the moderate time step restriction. Moreover, the adaptive DLN algorithms by the required error or numerical dissipation criterion are presented to balance the accuracy and computational cost. Numerical tests will be given to support the main conclusions. Comment: 35 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.02461 Zobrazit plný text záznamu View this record from Arxiv