论文标题
在不可压缩极限下针对正压欧拉系统的渐近保存和能量稳定方案
An Asymptotic Preserving and Energy Stable Scheme for the Barotropic Euler System in the Incompressible Limit
论文作者
论文摘要
设计和分析了低马赫数缩放下的Brotropic Euler系统的渐近保存和能量稳定方案。在对流通量中引入了与压力梯度成比例的速度变化，这导致机械能的耗散和所有马赫数的熵稳定性。时间和上风在空间全差异方案中的分辨率涉及两个步骤：解决密度的椭圆问题和速度的明确评估。所提出的方案具有多种物理相关的属性，例如密度的阳性，熵稳定性以及与连续欧拉系统弱公式的一致性。 The AP property of the scheme, i.e.\ the boundedness of the mesh parameters with respect to the Mach number and its consistency with the incompressible limit system, is shown rigorously.提出了广泛的案例研究的结果，以证实拟议方案的鲁棒性和功效以及理论主张。
An asymptotic preserving and energy stable scheme for the barotropic Euler system under the low Mach number scaling is designed and analysed. A velocity shift proportional to the pressure gradient is introduced in the convective fluxes, which leads to the dissipation of mechanical energy and the entropy stability at all Mach numbers. The resolution of the semi-implicit in time and upwind in space fully-discrete scheme involves two steps: solution of an elliptic problem for the density and an explicit evaluation for the velocity. The proposed scheme possess several physically relevant attributes, such as the positivity of density, the entropy stability and the consistency with the weak formulation of the continuous Euler system. The AP property of the scheme, i.e.\ the boundedness of the mesh parameters with respect to the Mach number and its consistency with the incompressible limit system, is shown rigorously. The results of extensive case studies are presented to substantiate the robustness and efficacy of the proposed scheme as well as the theoretical claims.
