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A high-order nodal discontinuous Galerkin method for solution of compressible non-cavitating and cavitating flows

机译：一种高阶节点不连续的Galerkin方法，用于可压缩的非空化和空化流溶液

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In this work, a high-order nodal discontinuous Galerkin method is applied and assessed for the simulation of compressible non-cavitating and cavitating flows. The one-fluid approach with the thermal effects is used to properly model the cavitation phenomenon. Here, the spatial and temporal derivatives in the system of governing equations are discretized using the nodal discontinuous Galerkin method and the third-order TVD Runge-Kutta method, respectively. Various numerical fluxes such as the Roe, Rusanov, HLL, HLLC and AUSM+-up and two discontinuity capturing methods, namely, the generalized MUSCL limiter and a generalized exponential filter are implemented in the solution algorithm. At first, the sinusoidal density wave problem which has a smooth solution is simulated and the effects of the numerical fluxes on the accuracy and performance of the nodal discontinuous Galerkin method are studied. Two problems, namely, the shock-density interaction (non-cavitating flow) and the two symmetric expansion waves (cavitating flow) are then computed and the effects of the numerical fluxes and the discontinuity capturing methods on the accuracy and computational cost of the solution are investigated. For non-cavitating flows, the high-pressure water-water shock tube and the low-pressure water-water shock tube are also simulated. Then, three cavitating flow problems, namely, the two symmetric expansion waves, the shock-condensation tube and the collapsing cavitation bubble are simulated to assess the accuracy and robustness of the solution algorithm. Results show that the solution methodology based on the high-order NDGM is accurate and robust for simulating the compressible non-cavitating and cavitating flows. (C) 2017 Elsevier Ltd. All rights reserved.
机译：在这项工作中，应用高阶节点不连续的Galerkin方法，并评估了可压缩的非空化和空化流的模拟。具有热效应的单流动方法用于适当地模拟空化现象。这里，控制方程系统中的空间和时间衍生物分别使用节点不连续的Galerkin方法和三阶TVD跑为库方法离散化。在解决方案算法中实现了各种数值磁通，包括ROE，RUSANOV，HLL，HLLC和AUSM + -UP和两个不连续性捕获方法，即，广义的Muscl限制器和广义指数滤波器。首先，模拟了具有光滑溶液的正弦密度波问题，研究了数值通量对节点不连续Galerkin方法的准确性和性能的影响。然后，然后计算抗冲击密度相互作用（非空化流量）和两个对称扩展波（空化流量）以及数值磁通量的效果和不连续性捕获方法对解决方案的准确性和计算成本的影响调查。对于非空化流动，还模拟了高压水 - 水冲击管和低压水 - 水冲击管。然后，模拟了三个空化的流动问题，即两个对称膨胀波，冲击冷凝管和塌陷的空化气泡以评估解决方案算法的精度和鲁棒性。结果表明，基于高阶NDGM的解决方案方法是准确且稳健的，用于模拟可压缩的非空化和空化流。 （c）2017 Elsevier Ltd.保留所有权利。

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