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High order finite-volume WENO scheme for five-equation model of compressible two-fluid flow

机译：可压缩两流体流五方程模型的高阶有限体积WENO格式

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摘要

High order finite-volume weighted essentially non-oscillatory (WENO) scheme is applied for solving interface-capturing five-equation model of compressible two-fluid flows in one and two-space dimensions. The model is non-conservative and the governing equations consist of three equations, namely a continuity equation, a momentum equation and an energy balance equation for the fluid mixture and the remaining two are mass and energy equations for one of the two fluids. In the last equation, the non-conservative differential source term appears which is responsible for the energy exchange between fluids. The energy exchange is only due to mechanical work. The presence of non-conservative differential source terms in the two-fluid flow model introduce difficulties in developing high order accurate numerical schemes. The proposed numerical scheme is capable to preserve non-oscillatory property near strong discontinuities and gives high order accuracy in smooth regions. Different one and two-dimensional test problems are considered to analyze efficiency and accuracy of the proposed numerical algorithms. For validation, the solutions of proposed numerical scheme are compared with the results of already available high order kinetic flux-vector splitting scheme and discontinuous Galerkin scheme. (C) 2018 Elsevier Ltd. All rights reserved.
机译：将高阶有限体积加权基本非振荡（WENO）方案用于求解一维和二维空间中可压缩两流体流的界面捕获五方程模型。该模型是非保守的，控制方程由三个方程组成，即流体混合物的连续性方程，动量方程和能量平衡方程，其余两个方程是两种流体之一的质量和能量方程。在最后一个方程中，出现了非保守的差分源项，该项负责流体之间的能量交换。能量交换仅是由于机械功。二流体流模型中非保守差分源项的存在为开发高阶精确数值方案带来了困难。所提出的数值方案能够在强不连续点附近保留非振荡特性，并在光滑区域中提供高阶精度。考虑了不同的一维和二维测试问题，以分析所提出数值算法的效率和准确性。为了进行验证，将提出的数值方案的解与已经可用的高阶动量矢量分裂方案和不连续Galerkin方案的结果进行了比较。 （C）2018 Elsevier Ltd.保留所有权利。

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