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首页> 外文期刊>Journal of Computational Physics >Numerical issues in gas flow dynamics with hydraulic shocks using high order finite volume WENO schemes
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Numerical issues in gas flow dynamics with hydraulic shocks using high order finite volume WENO schemes

机译：使用高阶有限卷Weno方案的液压冲击气流动力学的数值问题

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Accurate and efficient simulation of the hydraulic shock phenomenon in pipeline systems is of paramount importance. Even though the conservation-law formulation of the governing equations is here strongly advocated, the nonconservative form is still frequently used. This also concerns its mathematical conservative form. We investigated the numerical consequences of using the compressible gas flow model in the latter form while simulating a hydraulic shock. In this context, we also solved two Riemann problems. For the investigation, we used the third-, fifth- and seventh-order accurate weighted essentially non-oscillatory (WENO) scheme along with the Lax-Friedrichs solver at the cell interfaces. Both the classical finite volume WENO scheme and its modification WENO-Z have been implemented. A procedure based on the method of manufactured solutions has been developed to verify whether the numerical code solved correctly the hyperbolic set of equations. We demonstrated that the solutions of the conservative and nonconservative formulations are similar if we have smooth variations in the solution domain. The convective inertia term in the momentum equation should not be ignored. In the presence of shocks, differences in oscillating behavior and slope steepness near the discontinuities were observed. For the hydraulic shock problem, spurious oscillations appeared while using the nonconservative formulation in combination with the WENO-Z reconstruction. (C) 2019 Elsevier Inc. All rights reserved.
机译：管道系统中液压休克现象的准确有效模拟至关重要。尽管在这里强烈倡导控制方程的保守法制定，但仍然经常使用非必需的形式。这也涉及其数学保守形式​​。我们调查了在模拟液压冲击的同时使用后一种形式使用可压缩气体流动模型的数值后果。在这种情况下，我们还解决了两个riemann问题。对于调查，我们使用了基本上非振荡（Weno）方案的第三，第五次和第七顺序加权以及细胞界面的LAX-Friedrichs求解器。已经实施了经典有限卷Weno方案及其修改Weno-Z。已经开发了一种基于制造解决方案方法的过程，以验证数值代码是否正确解决了双曲线的方程集。我们证明，如果我们在溶液结构域中具有平滑的变化，保守和非官方配方的解决方案是相似的。不应忽视动量方程中的对流惯性术语。在存在冲击的情况下，观察到在不连续附近的振荡行为和斜坡陡度的差异。对于液压冲击问题，使用非必修制剂与Weno-Z重建结合使用的同时出现杂散振荡。 （c）2019 Elsevier Inc.保留所有权利。

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