BVD算法在可压缩多相流模拟中的实现
Implementation of BVD (boundary variation diminishing) algorithm in simulations of compressible multiphase flows
摘要：
本文提出了一种新的重构格式，即MUSCL-THINC-BVD格式，用于求解界面两相流的五方程模型。该方案采用了传统的激波捕捉MUSCL（守恒定律单调上游中心格式）方案以及界面锐化THINC（用于界面捕捉的双曲线切线）方案作为使用BVD进行空间重建的两个构建块（边界变化减小）原理，其最小化重构变量在单元边界处的变化（跳跃），从而有效地减少了数值解中的数值耗散。对所有状态变量和体积分数采用MUSCL-THINC-BVD格式，实现了体积分数与其它物理量的一致性。进行基准测试，以验证本方法的能力，在捕获的材料界面作为一个定义明确的急剧跳跃的体积分数，以及显着改善解决方案的质量。该格式是模拟可压缩界面多相流的一种简单有效的方法，具有实际意义。
英文摘要：
We present in this work a new reconstruction scheme, so-called MUSCL-THINC-BVD scheme, to solve the five-equation model for interfacial two phase flows. This scheme employs the traditional shock capturing MUSCL (Monotone Upstream-centered Schemes for Conservation Law) scheme as well as the interface sharpening THINC (Tangent of Hyperbola for INterface Capturing) scheme as two building-blocks of spatial reconstruction using the BVD (boundary variation diminishing) principle that minimizes the variations (jumps) of the reconstructed variables at cell boundaries, and thus effectively reduces the numerical dissipations in numerical solutions. The MUSCL-THINC-BVD scheme is implemented to all state variables and volume fraction, which realizes the consistency among volume fraction and other physical variables. Benchmark tests are carried out to verify the capability of the present method in capturing the material interface as a well-defined sharp jump in volume fraction, as well as significant improvement in solution quality. The proposed scheme is a simple and effective method of practical significance for simulating compressible interfacial multiphase flows.
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