TY - JOUR
T1 - An h-adaptive local discontinuous Galerkin method for the Navier-Stokes-Korteweg equations
AU - Tian, Lulu
AU - Xu, Yan
AU - Kuerten, J.G.M.
AU - van der Vegt, J.J.W.
N1 - Funding Information:
L. Tian acknowledges the China Scholarship Council (CSC) grant No. 2011634101 for giving the opportunity and financial support to study at the University of Twente in the Netherlands. Research of Yan Xu is supported by NSFC grant No. 11371342 , No. 11526212 . Research of J.J.W. van der Vegt was partially supported by the High-end Foreign Experts Recruitment Program ( GDW20157100301 ), while the author was in residence at the University of Science and Technology of China in Hefei, Anhui, China.
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/8/15
Y1 - 2016/8/15
N2 - 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.
AB - 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.
KW - (Non)-isothermal Navier-Stokes-Korteweg equations
KW - Accuracy and stability
KW - Local discontinuous Galerkin method
KW - Mesh adaptation
KW - Solid wall boundaries
KW - 2023 OA procedure
UR - http://www.scopus.com/inward/record.url?scp=84969651840&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2016.05.027
DO - 10.1016/j.jcp.2016.05.027
M3 - Article
SN - 0021-9991
VL - 319
SP - 242
EP - 265
JO - Journal of computational physics
JF - Journal of computational physics
ER -