An h-adaptive local discontinuous Galerkin method for the Navier-Stokes-Korteweg equations

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• 作者：Lulu Tian^a ; ^b ; ^{18661997061@163.com" class="auth_mail" title="E-mail the corresponding author} ; Yan Xu^c ; ^{yxu@ustc.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; J.G.M. Kuerten^b ; ^d ; ^{J.G.M.Kuerten@tue.nl" class="auth_mail" title="E-mail the corresponding author} ; J.J.W. van der Vegt^b ; ^{j.j.w.vandervegt@utwente.nl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Local discontinuous Galerkin method ; Mesh adaptation ; (Non)-isothermal Navier&ndash ; Stokes&ndash ; Korteweg equations ; Solid wall boundaries ; Accuracy and stability
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 August 2016
• 年：2016
• 卷：319
• 期：Complete
• 页码：242-265
• 全文大小：7000 K

文摘

In this article, we develop a mesh adaptation algorithm for a local discontinuous Galerkin (LDG) discretization of the (non)-isothermal Navier–Stokes–Korteweg (NSK) equations modeling liquid–vapor flows with phase change. This work is a continuation of our previous research, where we proposed LDG discretizations for the (non)-isothermal NSK equations with a time-implicit Runge–Kutta method. To save computing time and to capture the thin interfaces more accurately, we extend the LDG discretization with a mesh adaptation method. Given the current adapted mesh, a criterion for selecting candidate elements for refinement and coarsening is adopted based on the locally largest value of the density gradient. A strategy to refine and coarsen the candidate elements is then provided. We emphasize that the adaptive LDG discretization is relatively simple and does not require additional stabilization. The use of a locally refined mesh in combination with an implicit Runge–Kutta time method is, however, non-trivial, but results in an efficient time integration method for the NSK equations. Computations, including cases with solid wall boundaries, are provided to demonstrate the accuracy, efficiency and capabilities of the adaptive LDG discretizations.