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An implicit dual-time stepping high-order nodal discontinuous Galerkin method for solving incompressible flows on triangle elements

Hajihassanpour, M ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1016/j.matcom.2019.08.011
  3. Publisher: Elsevier B.V , 2020
  4. Abstract:
  5. In this work, a high-order nodal discontinuous Galerkin method (NDGM) is developed and assessed for the simulation of 2D incompressible flows on triangle elements. The governing equations are the 2D incompressible Navier–Stokes equations with the artificial compressibility method. The discretization of the spatial derivatives in the resulting system of equations is made by the NDGM and the time integration is performed by applying the implicit dual-time stepping method. Three numerical fluxes, namely, the local Lax–Friedrich, Roe and AUSM+-up are formulated and applied to assess and compare their accuracy and performance in the simulation of incompressible flows using the NDGM. Several steady and unsteady incompressible flow problems are simulated to examine the accuracy and robustness of the proposed solution methodology and they are the Kovasznay, backward facing step, NACA0012 airfoil, circular cylinder and two side-by-side circular cylinders. Indications are that the NDGM applied for solving the incompressible Navier–Stokes equations with the artificial compressibility approach and the implicit dual-time stepping method is accurate and robust for the simulation of steady and unsteady incompressible flow problems. © 2019 International Association for Mathematics and Computers in Simulation (IMACS)
  6. Keywords:
  7. Artificial compressibility method ; Implicit dual-time stepping method ; Incompressible flows ; Nodal discontinuous Galerkin method ; Numerical flux ; Triangle elements ; Circular cylinders ; Compressibility ; Galerkin methods ; Navier Stokes equations ; Numerical methods ; Artificial compressibility approach ; Backward facing step ; Dual time stepping method ; Nodal discontinuous galerkin methods ; Solution methodology ; System of equations ; Incompressible flow
  8. Source: Mathematics and Computers in Simulation ; Volume 168 , 2020 , Pages 173-214
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0378475419302514