A Non-oscillatory Multi-Moment Finite Volume Scheme with Boundary Gradient Switching
A Non-oscillatory Multi-Moment Finite Volume Scheme with Boundary Gradient Switching
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DOI：
10.1007/s10915-017-0392-0
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发表时间：
2017-02
影响因子：
2.5
通讯作者：
X. Deng;Ziyao Sun;B. Xie;K. Yokoi;Chungang Chen;F. Xiao
中科院分区：
文献类型：
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作者：
X. Deng;Ziyao Sun;B. Xie;K. Yokoi;Chungang Chen;F. Xiao
在这项工作中，我们提出了一个新的高阶多矩约束有限体积（MCV）方法。在一维积木格式中，三个局部自由度（DOF）被等距地定义在一个网格单元内。该方法通过在相邻单元中增加一个约束条件，即左右相邻单元中点处的自由度，构造了两个三阶空间重构的候选多项式。基于变分最小化原理设计了一种边界梯度切换（BGS）算法来确定两个候选点的空间重构，以消除不连续点周围的伪振荡。所得到的无振荡MCV 3-BGS格式具有四阶精度，且完全不含与情况相关的自组织参数。通过对一维和二维标量守恒律和欧拉双曲守恒律的基准测试，验证了本文提出的格式的性能。MCV 3-BGS格式具有精度高、无振荡、算法简单等优点，在实际应用中具有很好的应用前景。
In this work we propose a new formulation for high-order multi-moment constrained finite volume (MCV) method. In the one-dimensional building-block scheme, three local degrees of freedom (DOFs) are equidistantly defined within a grid cell. Two candidate polynomials for spatial reconstruction of third-order are built by adopting one additional constraint condition from the adjacent cells, i.e. the DOF at middle point of left or right neighbour. A boundary gradient switching (BGS) algorithm based on the variation-minimization principle is devised to determine the spatial reconstruction from the two candidates, so as to remove the spurious oscillations around the discontinuities. The resulted non-oscillatory MCV3-BGS scheme is of fourth-order accuracy and completely free of case-dependent ad hoc parameters. The widely used benchmark tests of one- and two-dimensional scalar and Euler hyperbolic conservation laws are solved to verify the performance of the proposed scheme in this paper. The MCV3-BGS scheme is very promising for the practical applications due to its accuracy, non-oscillatory feature and algorithmic simplicity.