Density based finite volume schemes usually used for the computation of compressible flows are known to be, in general, not accurate in the low Mach number limit. A very popular low Mach number fix that has been proposed in different forms consists in centring the gradient of the pressure. In this article, we first perform some numerical experiments for proving that this low Mach number fix may lead to non-convergence on the momentum, especially if unstructured meshes are used. We also show that on the long time limit of the wave system, the same kind of problem may occur.On triangular meshes, we perform a full analysis of the spurious modes of the wave system, and make evidence that the numerical scheme exhibits some oscillatory spurious modes. On simple triangular mesh configurations, these spurious modes are explicitly built. Then on general triangular meshes, we explain how to compute a basis of the spurious modes by relying on the ones built on simple configurations. A major outcome of this article is that the dimension of the spurious modes space is very large, approximately equal to the number of nodes of the mesh.

To survey cancer-related mutations in human pluripotent stem cells and their derivatives, we analyzed >2,200 transcriptomes from 146 independent lines in the NCBI’s Sequence Read Archive. Twenty-two per cent of samples had at least one cancer-related mutation; of these, 64% had TP53 mutations, which conferred a pronounced selective advantage, perturbed target gene expression and altered cellular differentiation. These findings underscore the need for robust surveillance of cancer-related mutations in pluripotent cells, especially in clinical applications.

In this article, we address the problem of accuracy of finite volume schemes in the low Mach number limit. It has been known for years collocated finite volume schemes are naturally correctly behaving in this limit on triangular meshes [21,22,16], but fail in general on other of mesh. We are first interested in the general problem of the conservation of vorticity for the wave system. By enriching the approximation for vectors, we prove that the Hodge-Helmholtz context developed for triangular meshes in [16] can be recovered in the quadrangular mesh This leads to a numerical scheme for the wave system that naturally preserves the vorticity under mild assumption on the numerical flux. The approximation space is then used with the barotropic Euler system. Numerical tests show that the new numerical scheme is accurate for both steady and acoustic problems at low Mach number.

In this article, we are interested in the behavior of discontinuous Galerkin schemes for compressible flows in the low Mach number limit. We prove that for any numerical flux conserving exactly contacts (e.g., exact Godunov, Roe, HLLC), the numerical scheme is accurate at low Mach number flows on simplicial meshes, which is an extension to higher order of the result proven in [H. Guillard, Comput. Fluids, 38 (2009), pp. 1969-1972]. When the mesh is not simplicial, or when the mesh is simplicial but the numerical flux does not conserve contacts (e.g., Lax -Friedrich, HLL), the scheme is numerically proven to be less accurate in the low Mach number limit.

We propose to extend the fix of Roe’s approximate Riemann solver developed for the Barotropic Euler equations in [2] to the full Euler equations. This scheme is built mainly to handle low Mach acousticwaves. Moreover, compared to pressure-centered type schemes, this numerical fix has the advantage of improving the numerical solution in the sense that the oscillating modes are reduced. The theoretical study is based on a two-time scales asymptotic analysis. It is proved that the Euler system equipped with a general equation of state is consistent with a first-order wave system in a low Mach number regime. Similar analysis is performed at the discrete level on the Roe scheme to derive the new fix. Numerical tests confirm the results obtained for the Barotropic case about the ability of this fix to deal with both steady and low Mach acoustic computations also in the case of full Euler equations.

This article is dedicated to the long time behavior of a finite volume approximation of general symmetrizable linear hyperbolic system on a bounded domain. In the continuous case this problem is very difficult, and the omega-limit set (namely the set of all the possible long time limits) may be large and complicated to depict if no dissipation is introduced. In this article we prove that in general, with a stable finite volume scheme, the discrete solution converges to a steady state when the time goes to infinity. This property is a direct consequence of the numerical dissipation mechanisms used for stabilizing the discretization. We apply this result for determining the long time limit for several stabilizations of the wave system, and perform a formal link with the low Mach number problem of the nonlinear Euler system. Numerical experiments with the wave system are performed for confirming the theoretical results obtained.

ThisJung, Jonathan paperLannabi, Ibtissem deals withPerrier, Vincent the numerical resolution of a linear wave system using the Godunov scheme with a centered discretization of the pressure gradient. The interest in such schemes is motivated by the low Mach number accuracy problem. We prove that for both steady and unsteady flows, an oscillatory mode appears in the numerical solution. This can be explained by the loss of the Total Variation Diminishing property on the characteristic variables. Moreover, we illustrate numerically that the long-time numerical solution includes an oscillatory mode, which jeopardizes the convergence towards the expected solution.

The aim of this article is to thoroughly identify the spurious mode that jeopardizes the convergence of usual upwind numerical schemes for compressible flows when the Mach number goes to 0. We show that this spurious mode is the long time limit of a wave system whose properties and discretization depend on the scheme used for the compressible system. Once this spurious mode is identified, a filtering method is developed for removing it from the solution of stationary low Mach number compressible flow. Numerical results confirm that at the price of the computation of a long time solution of the wave system, the accuracy of an inaccurate solution of a low Mach number compressible flow can be greatly improved by this filtering method.

The aim of this article is to thoroughly identify the spurious mode that jeopardizes the convergence of usual upwind numerical schemes for compressible flows when the Mach number goes to 0. We show that this spurious mode is the long time limit of a wave system whose properties and discretization depend on the scheme used for the compressible system. Once this spurious mode is identified, a filtering method is developed for removing it from the solution of stationary low Mach number compressible flow. Numerical results confirm that at the price of the computation of a long time solution of the wave system, the accuracy of an inaccurate solution of a low Mach number compressible flow can be greatly improved by this filtering method. • Link between the low Mach number problem and the long time behavior of the wave system. • Exact identification of the spurious mode for low Mach number flows. • A filtering method is developed, able to compute low Mach stationary flows.

Classical finite volume schemes for the Euler system are not accurate at low Mach number and some fixes have to be used and were developed in a vast literature over the last two decades. The question we are interested in in this article is: What about if the porosity is no longer uniform? We first show that this problem may be understood on the linear wave equation taking into account porosity. We explain the influence of the cell geometry on the accuracy property at low Mach number. In the triangular case, the stationary space of the Godunov scheme approaches well enough the continuous space of constant pressure and divergence-free velocity, while this is not the case in the Cartesian case. On Cartesian meshes, a fix is proposed and accuracy at low Mach number is proved to be recovered. Based on the linear study, a numerical scheme and a low Mach fix for the non-linear system, with a non-conservative source term due to the porosity variations, is proposed and tested.