A low Mach correction able to deal with low Mach acoustic and free of checkerboard modes

National audienceIt is well known that finite volume schemes are not accurate at low Mach number in the sense that they do not allow to obtain the incompressible limit when the Mach number is small on Cartesian meshes [4]. Increase the order of the method with a Discontinous Galerkin method is not sufficient to get the accuracy at low Mach number [1]. The schemes needs corrections [4, 5, 3, 2]. These corrections aim at reducing the numerical diffusion of the scheme to obtain accurate schemes for flows near the incompressible limit but could induce checkerboard modes [5, 2]. Moreover, since this diffusion is necessary to stabilize the scheme, it is also interesting to focus on the accuracy of the scheme at low Mach number with respect to the acoustic part of the solution. We will present a corrected scheme that is accurate at low Mach number for steady and unsteady flows, has the same CFL restriction as the Roe scheme for an explicit time integration and is free of checkerboard modes

Behaviour of upwind schemes in low Mach number flow

International audienceIn the present work, we are interested in the direct numerical simulation of the compressible Euler and Navier Stokes equations at low Mach number regime. First, we propose a review of existing work on the subject in order to identify the issues raised by the simulation of in this kind of flow, and the existing relevant solutions. Then, we will test different selected compressible low Mach solvers using the discontinuous Galerkin space discretisation and discuss about their behaviour

High-order Discontinuous Galerkin Solutions of Internal Low-mach Number Turbulent Flows☆

Abstract In this work we apply the high-order Discontinuous Galerkin (DG) finite element method to internal low-Mach number turbulent flows. The method here presented is designed to improve the performance of the solution in the incompressible limit using an implicit scheme for the temporal integration of the compressible Reynolds Averaged Navier Stokes (RANS) equations. The per- formance of the scheme is demonstrated by solving a well-known test-case consisting of an abrupt axisymmetric expansion using various degrees of polynomial approximation. Computations with k–ω model are performed to assess the modelling capabilities, with high-order accurate DG discretizations of the RANS equations, in presence of non-equilibrium flow conditions

Low-Mach number treatment for Finite-Volume schemes on unstructured meshes

The paper presents a low-Mach number (LM) treatment technique for high-order, Finite-Volume (FV) schemes for the Euler and the compressible Navier–Stokes equations. We concentrate our efforts on the implementation of the LM treatment for the unstructured mesh framework, both in two and three spatial dimensions, and highlight the key differences compared with the method for structured grids. The main scope of the LM technique is to at least maintain the accuracy of low speed regions without introducing artefacts and hampering the global solution and stability of the numerical scheme. Two families of spatial schemes are considered within the k-exact FV framework: the Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and the Weighted Essentially Non-Oscillatory (WENO). The simulations are advanced in time with an explicit third-order Strong Stability Preserving (SSP) Runge–Kutta method. Several flow problems are considered for inviscid and turbulent flows where the obtained solutions are compared with referenced data. The associated benefits of the method are analysed in terms of overall accuracy, dissipation characteristics, order of scheme, spatial resolution and grid composition

A discontinuous Galerkin method for inviscid low Mach number flows

In this work we extend the high-order Discontinuous Galerkin (DG) Finite element method to inviscid low Mach number flows. The method here presented is designed to improve the accuracy and efficiency of the solution at low Mach numbers using both explicit and implicit schemes for the temporal discretization of the compressible Euler equations. The algorithm is based on a classical preconditioning technique that in general entails modifying both the instationary term of the governing equations and the dissipative term of the numerical flux function (full preconditioning approach). In the paper we show that full preconditioning is beneficial for explicit time integration while the implicit scheme turns out to be efficient and accurate using just the modified numerical flux function. Thus the implicit scheme could also be used for time accurate computations. The performance of the method is demonstrated by solving an inviscid flow past a NACA0012 airfoil at different low Mach numbers using various degrees of polynomial approximations. Computations with and without preconditioning are performed on different grid topologies to analyze the influence of the spatial discretization on the accuracy of the DG solutions at low Mach numbers

A low Mach correction able to deal with low Mach acoustics

International audienceThis article deals with acoustic computations in low Mach number flows with density based solvers. For ensuring a good resolution of the low Mach number base flow, a scheme able to deal with stationary low Mach number flows is necessary. Previously proposed low Mach number fixes are tested with acoustic computations. Numerical results prove that they are not accurate for acoustic computations. The issues raised with acoustic computations with low Mach number fixes are discussed, and a new scheme is developed, in order to be accurate not only for steady low Mach number flows, but also for acoustic computations. Numerical tests show the improvement of the proposed scheme with respect to the state of the art

A discontinuous Galerkin method for inviscid low Mach number flows

In this work we extend the high-order discontinuous Galerkin (DG) finite element method to inviscid low Mach number flows. The method here presented is designed to improve the accuracy and efficiency of the solution at low Mach numbers using both explicit and implicit schemes for the temporal discretization of the compressible Euler equations. The algorithm is based on a classical preconditioning technique that in general entails modifying both the instationary term of the governing equations and the dissipative term of the numerical flux function (full preconditioning approach). In the paper we show that full preconditioning is beneficial for explicit time integration while the implicit scheme turns out to be efficient and accurate using just the modified numerical flux function. Thus the implicit scheme could also be used for time accurate computations. The performance of the method is demonstrated by solving an inviscid flow past a NACA0012 airfoil at different low Mach numbers using various degrees of polynomial approximations. Computations with and without preconditioning are performed on different grid topologies to analyze the influence of the spatial discretization on the accuracy of the DG solutions at low Mach numbers. © 2009 Elsevier Inc. All rights reserved