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Implementation of a low-mach number modification for high-order finite-volume schemes for arbitrary hybrid unstructured meshes

机译:针对任意混合非结构化网格的高阶有限体积方案的低马赫数修改的实现

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摘要

An implementation of a novel low-mach number treatment for high-order finite-volume schemes using arbitrary hybrid unstructured meshes is presented in this paper. Low-Mach order modifications for Godunov type finite-volume schemes have been implemented successfully for structured and unstructured meshes, however the methods break down for hybrid mesh topologies containing multiple element types. The modification is applied to the UCNS3D finite-volume framework for compressible flow configurations, which have been shown as very capable of handling any type of grid topology. The numerical methods under consideration are the Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and the Weighted Essentially Non-Oscillatory (WENO) schemes for two-dimensional mixed-element type unstructured meshes. In the present study the HLLC Approximate Riemann Solver is used with an explicit TVD Runge-Kutta 3rd-order method due to its excellent scalability. These schemes (up to 5th-order) are applied to well established two-dimensional and three-dimensional test cases. The challenges that occur when applying these methods to low-mach flow configurations is thoroughly analysed and possible improvements and further test cases are suggested.
机译:本文提出了一种使用任意混合非结构化网格的高阶有限体积方案的新型低马赫数处理方法。 Godunov型有限体积方案的低马赫数阶修改已成功地应用于结构化网格和非结构化网格,但是对于包含多种元素类型的混合网格拓扑,该方法无法实现。该修改被应用于可压缩流配置的UCNS3D有限体积框架,该框架已显示出能够处理任何类型的网格拓扑。所考虑的数值方法是用于混合法类型的二维非结构化网格的单调上游守恒定律方案(MUSCL)和加权基本非振荡(WENO)方案。在本研究中,由于其出色的可扩展性,HLLC近似黎曼求解器与显式TVD Runge-Kutta三阶方法一起使用。这些方案(最多5阶)适用于完善的二维和三维测试用例。彻底分析了将这些方法应用于低马赫数流量配置时出现的挑战,并提出了可能的改进和进一步的测试案例。

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