Duality based boundary conditions and dual consistent finite difference discretizations of the Navier-Stokes and Euler equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:259

Article

Berg, Jens¹  Nordstrom, Jan² 

[1] Uppsala Univ, Dept Informat Technol, SE-75105 Uppsala, Sweden

[2] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden

关键词: High-order finite differences;    Summation-by-parts;    Superconvergence;    Boundary conditions;    Dual consistency;    Stability;   

DOI  :  10.1016/j.jcp.2013.11.031

来源: Elsevier

【 摘 要 】

In this paper we derive new far-field boundary conditions for the time-dependent Navier-Stokes and Euler equations in two space dimensions. The new boundary conditions are derived by simultaneously considering well-posedness of both the primal and dual problems. We moreover require that the boundary conditions for the primal and dual Navier-Stokes equations converge to well-posed boundary conditions for the primal and dual Euler equations. We perform computations with a high-order finite difference scheme on summation-by-parts form with the new boundary conditions imposed weakly by the simultaneous approximation term. We prove that the scheme is both energy stable and dual consistent and show numerically that both linear and non-linear integral functionals become superconvergent. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free