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Finite-volume WENO scheme for viscous compressible multicomponent flows

机译：粘性可压缩多组分流的有限体积WENO方案

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摘要

We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin.
机译：我们开发了一种震荡和界面捕获数值方法，适用于模拟由可压缩Navier-Stokes方程控制的多组分流动。数值方法在流动的平滑区域中是高阶精度的，离散地保留了每个分量的质量以及总动量和能量，并且是无振荡的，即它不会在冲击波的位置引入杂散振荡和/或材料界面。该方法是Godunov型的，并采用五阶有限体积加权基本非振荡（WENO）方案进行空间重建，并使用Harten-Lax-van Leer接触（HLLC）近似Riemann求解器来使通量迎风。采用三阶总变差递减（TVD）Runge-Kutta（RK）算法来按时进行求解。该推导被推广到三个维度和不均匀的笛卡尔网格。利用两点四阶高斯正交规则建立单元内部以及单元边界处重构变量的空间平均值。因此，该算法在空间的平滑区域中的空间精度为四阶，时间上的精度为三阶。通过考虑几个具有挑战性的一维，二维和三维测试案例，我们证实了数值方法的性质，其中最复杂的是淹没在圆柱形水腔中的气泡的不对称坍塌，而水腔中嵌入了10％的明胶。

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