标题： 一种适用于欧拉和纳维-斯托克斯方程的渐近保持全速度格式 显示英文标题

标题： An Asymptotic-Preserving all-speed scheme for the Euler and Navier-Stokes equations

摘要： 我们提出了一种渐近保持的“全速度”方案，用于模拟从非常小到单位量级的所有马赫数范围内的可压缩流体。 该方案基于半隐式离散化，其中声学部分是隐式处理的，对流和扩散部分是显式处理的。 这种离散化是渐近保持特性的关键，它提供了对双曲可压缩区和椭圆不可压缩区的一致近似。 在不可压缩区，速度的散度为零条件得到尊重，并且通过动量和能量方程的适当组合得到的椭圆方程计算压力。 声学部分的隐式处理使得时间步长与马赫数无关。 该方案是守恒的，适用于稳态或非稳态流动以及一般的状态方程。 一维和二维数值结果验证了渐近保持的“全速度”特性。 显示英文摘要

摘要： We present an Asymptotic-Preserving 'all-speed' scheme for the simulation of compressible flows valid at all Mach-numbers ranging from very small to order unity. The scheme is based on a semi-implicit discretization which treats the acoustic part implicitly and the convective and diffusive parts explicitly. This discretization, which is the key to the Asymptotic-Preserving property, provides a consistent approximation of both the hyperbolic compressible regime and the elliptic incompressible regime. The divergence-free condition on the velocity in the incompressible regime is respected, and an the pressure is computed via an elliptic equation resulting from a suitable combination of the momentum and energy equations. The implicit treatment of the acoustic part allows the time-step to be independent of the Mach number. The scheme is conservative and applies to steady or unsteady flows and to general equations of state. One and Two-dimensional numerical results provide a validation of the Asymptotic-Preserving 'all-speed' properties.