A high‐order discontinuous Galerkin solver for low Mach number flows. (9th December 2015)

• Record Type: Journal Article
• Authors: Klein, B.; Müller, B.; Kummer, F.; Oberlack, M.
• Is Part Of: International journal for numerical methods in fluids. Volume 81:Number 8(2016)
• Page Start: 489
• Page End: 520
• Publication Date: 2015-12-09
• Subjects: finite element -- discontinuous Galerkin -- Navier–Stokes -- low Mach -- variable density flows -- SIMPLE algorithm; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4193
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: In this work, we present a high‐order discontinuous Galerkin method (DGM) for simulating variable density flows at low Mach numbers. The corresponding low Mach number equations are an approximation of the compressible Navier–Stokes equations in the limit of zero Mach number. To the best of the authors'y knowledge, it is the first time that the DGM is applied to the low Mach number equations. The mixed‐order formulation is applied for spatial discretization. For steady cases, we apply the semi‐implicit method for pressure‐linked equation (SIMPLE) algorithm to solve the non‐linear system in a segregated manner. For unsteady cases, the solver is implicit in time using backward differentiation formulae, and the SIMPLE algorithm is applied to solve the non‐linear system in each time step. Numerical results for the following three test cases are shown: Couette flow with a vertical temperature gradient, natural convection in a square cavity, and unsteady natural convection in a tall cavity. Considering a fixed number of degrees of freedom, the results demonstrate the benefits of using higher approximation orders. Copyright © 2015 John Wiley & Sons, Ltd. Abstract : We present a high‐order discontinuous Galerkin method for simulating variable density flows at low Mach numbers. The solver is based on the lowMach number equations, which are an approximation of the compressible Navier–Stokes equations in the limit of zero Mach number. Numerical tests for Couette flow with a vertical temperature gradient and natural convection in enclosed cavities confirm the high accuracy of the method.