Preserving Nonnegativity in Discontinuous Galerkin Approximations to Scalar Transport via Truncation and Mass Aware Rescaling (TMAR)
Preserving Nonnegativity in Discontinuous Galerkin Approximations to Scalar Transport via Truncation and Mass Aware Rescaling (TMAR)
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DOI：
10.1175/mwr-d-16-0220.1
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发表时间：
2016-11
影响因子：
3.2
通讯作者：
Devin K. Light;D. Durran
中科院分区：
文献类型：
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作者：
Devin K. Light;D. Durran
摘要针对标量平流方程的不连续伽辽金离散，给出了一种精确的非负保持限制器。通过应用质量保守限制器来保留示踪剂场的非负性，该限制器截断每个元素内的负性，并线性重新缩放所得DG多项式以保持元素平均质量。作为初步步骤，通过单元每侧的DG通量以类似于通量校正输运的方式进行限制，以确保单元平均质量在时间积分的每个单独阶段保持非负。本文证明了这种截断和质量感知重标（TMAR）不会改变底层无限DG近似的精度阶数。二维变形流的数值试验表明，该方法在保持非负性的同时，精度高，效率高。与以前流行的一些方法相比，TMAR限制特别好……
AbstractAn accurate nonnegativity preserving limiter is presented for use with discontinuous Galerkin (DG) discretizations of scalar advection equations. The nonnegativity of the tracer field is preserved through the application of a mass conservative limiter that truncates negatives within each element and linearly rescales the resulting DG polynomials to preserve element-mean mass. As a preliminary step, the DG fluxes through each side of the element are limited in a manner similar to flux-corrected transport to ensure that the element-mean mass remains nonnegative during each individual stage of the time integration. In this paper, it is proven that such a truncation and mass aware rescaling (TMAR) does not change the order of accuracy of the underlying unlimited DG approximation. Numerical tests with two-dimensional deforming flows confirm that the method remains accurate and efficient while preserving nonnegativity. In comparison to some popular previous approaches, TMAR limiting is particularly well...