Temporal error analysis of a new Euler semi-implicit scheme for the incompressible Navier-Stokes equations with variable density

摘要

Based upon an equivalent form of the incompressible Navier-Stokes equations with variable density, a first-order backward Euler time-discrete scheme is studied for solving the variable density flows numerically. The proposed numerical scheme is unconditionally stable. A rigorous error analysis is presented and the first-order temporal convergence rate O(r) is proved without any assumption on numerical solution by using the discrete maximal Lp-regularity of the Stokes problem, where r is the time step size. Some numerical results are provided to confirm our theoretical analysis. (c) 2022 Elsevier B.V. All rights reserved.