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首页> 外文期刊>Journal of Computational Physics >Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws
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Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws

机译：不连续Galerkin的逐点分层重构和求解守恒律的有限体积方法

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摘要

We develop a new hierarchical reconstruction (HR) method [17,28] for limiting solutions of the discontinuous Galerkin and finite volume methods up to fourth order of accuracy without local characteristic decomposition for solving hyperbolic nonlinear conservation laws on triangular meshes. The new HR utilizes a set of point values when evaluating polynomials and remainders on neighboring cells, extending the technique introduced in Hu, Li and Tang [9]. The point-wise HR simplifies the implementation of the previous HR method which requires integration over neighboring cells and makes HR easier to extend to arbitrary meshes. We prove that the new point-wise HR method keeps the order of accuracy of the approximation polynomials. Numerical computations for scalar and system of nonlinear hyperbolic equations are performed on two-dimensional triangular meshes. We demonstrate that the new hierarchical reconstruction generates essentially non-oscillatory solutions for schemes up to fourth order on triangular meshes.
机译：我们开发了一种新的层次重构（HR）方法[17,28]，用于将不连续的Galerkin方法和有限体积方法的求解限制到四阶精度，而无需局部特征分解，从而解决了三角网格上的双曲非线性守恒律。新的HR在评估多项式和相邻单元格上的余数时利用了一组点值，扩展了Hu，Li和Tang [9]中引入的技术。点式HR简化了以前的HR方法的实现，该方法需要在相邻单元上进行集成，并使HR易于扩展到任意网格。我们证明了新的逐点HR方法保持了近似多项式精度的顺序。在二维三角形网格上对非线性双曲方程的标量和系统进行数值计算。我们证明了新的分层重建为三角形网格上的四阶方案生成了基本上无振荡的解。

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