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首页> 外文期刊>Journal of Computational Physics >A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations
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A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations

机译：可压缩Navier-Stokes方程的低数值耗散沉浸接口方法

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摘要

A numerical method to solve the compressible Navier-Stokes equations around objects of arbitrary shape using Cartesian grids is described. The approach considered here uses an embedded geometry representation of the objects and approximate the governing equations with a low numerical dissipation centered finite-difference discretization. The method is suitable for compressible flows without shocks and can be classified as an immersed interface method. The objects are sharply captured by the Cartesian mesh by appropriately adapting the discretization stencils around the irregular grid nodes, located around the boundary. In contrast with available methods, no jump conditions are used or explicitly derived from the boundary conditions, although a number of elements are adopted from previous immersed interface approaches. A new element in the present approach is the use of the summation-by-parts formalism to develop stable non-stiff first-order derivative approximations at the irregular grid points. Second-order derivative approximations, as those appearing in the transport terms, can be stiff when irregular grid points are located too close to the boundary. This is addressed using a semi-implicit time integration method. Moreover, it is shown that the resulting implicit equations can be solved explicitly in the case of constant transport properties. Convergence studies are performed for a rotating cylinder and vortex shedding behind objects of varying shapes at different Mach and Reynolds numbers.
机译：描述了一种使用笛卡尔网格求解围绕任意形状物体的可压缩Navier-Stokes方程的数值方法。这里考虑的方法使用对象的嵌入式几何表示形式，并以低数值耗散为中心的有限差分离散化近似控制方程。该方法适用于无冲击的可压缩流动，可以归类为沉浸式界面方法。通过适当地调整位于边界附近的不规则网格节点周围的离散化模具，笛卡尔网格可以清晰地捕获对象。与现有方法相反，尽管先前的沉浸式界面方法采用了许多元素，但并未使用跳变条件或未从边界条件中明确得出跳跃条件。本方法中的一个新元素是使用按部分求和的形式主义来在不规则网格点处开发稳定的非刚性一阶导数近似。当不规则网格点的位置离边界太近时，二阶导数近似（如在运输项中出现的近似）可能会变得僵硬。这是使用半隐式时间积分方法解决的。此外，还表明，在恒定输运性质的情况下，可以明确求解得到的隐式方程。对旋转的圆柱体进行了收敛研究，并以不同的马赫数和雷诺数在不同形状的物体后面涡旋脱落。

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