Monoslope and multislope MUSCL methods for unstructured meshes
Monoslope and multislope MUSCL methods for unstructured meshes
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DOI：
10.1016/j.jcp.2010.01.026
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发表时间：
2010-05
期刊：
影响因子：
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通讯作者：
T. Buffard;S. Clain
中科院分区：
文献类型：
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作者：
T. Buffard;S. Clain
我们提出了与三角网格上的网格中心有限体积法相关的新的MUSCL技术。第一次重建包括通过关于规定的稳定性条件的最小化过程来计算每个控制体的一个矢量斜率。我们提出的第二种技术是基于每个三角形(每条边一个)三个标量斜率的计算，仍然考虑了一些稳定性条件。所得到的算法提供了一个非常简单的方案，该方案可扩展到高维问题。数值逼近被用来获得平流标量问题的收敛阶，而我们处理一个非线性向量例子，即欧拉系统，以显示新的MUSCL技术处理更复杂情况的能力。
We present new MUSCL techniques associated with cell-centered finite volume method on triangular meshes. The first reconstruction consists in calculating one vectorial slope per control volume by a minimization procedure with respect to a prescribed stability condition. The second technique we propose is based on the computation of three scalar slopes per triangle (one per edge) still respecting some stability condition. The resulting algorithm provides a very simple scheme which is extensible to higher dimensional problems. Numerical approximations have been performed to obtain the convergence order for the advection scalar problem whereas we treat a nonlinear vectorial example, namely the Euler system, to show the capacity of the new MUSCL technique to deal with more complex situations.