A dual consistent summation-by-parts formulation for the linearized incompressible Navier-Stokes equations posed on deforming domains

JOURNAL OF COMPUTATIONAL PHYSICS

卷:376

Article

Nikkar, Samira¹  Nordstrom, Jan¹ 

[1] Linkoping Univ, Dept Math, Computat Math, SE-58183 Linkoping, Sweden

关键词: Incompressibl Navier-Stokes equations;    Deforming domain;    Stability;    Dual consistency;    High order accuracy;    Superconvergence;   

DOI  :  10.1016/j.jcp.2018.09.006

来源: Elsevier

【 摘 要 】

In this article, well-posedness and dual consistency of the linearized constant coefficient incompressible Navier-Stokes equations posed on time-dependent spatial domains are studied. To simplify the derivation of the dual problem and improve the accuracy of gradients, the second order formulation is transformed to first order form. Boundary conditions that simultaneously lead to boundedness of the primal and dual problems are derived. Fully discrete finite difference schemes on summation-by-parts form, in combination with the simultaneous approximation technique, are constructed. We prove energy stability and discrete dual consistency and show how to construct the penalty operators such that the scheme automatically adjusts to the variations of the spatial domain. As a result of the aforementioned formulations, stability and discrete dual consistency follow simultaneously. The method is illustrated by considering a deforming time-dependent spatial domain in two dimensions. The numerical calculations are performed using high order operators in space and time. The results corroborate the stability of the scheme and the accuracy of the solution. We also show that linear functionals are superconverging. Additionally, we investigate the convergence of non-linear functionals and the divergence of the solution. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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