Restoration of the contact surface in FORCE-type centred schemes II: Non-conservative one- and two-layer two-dimensional shallow water equations
Restoration of the contact surface in FORCE-type centred schemes II: Non-conservative one- and two-layer two-dimensional shallow water equations
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FORCE型中心格式中接触面的恢复II：非保守一、两层二维浅水方程
DOI：
10.1016/j.advwatres.2012.03.018
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发表时间：
2012
影响因子：
4.7
通讯作者：
E. Toro
中科院分区：
文献类型：
--
作者：
A. Canestrelli;E. Toro
近年来，针对可压缩多相流的浅水方程[4]、Pitman和Le的双流体流动模型[17]、二维和三维Baer-Nunziato方程[17]等多维非保守方程，提出了一种非保守的良好平衡力型格式。在本文中，首先将原始格式改写为一种适合的形式，使数值通量易于操作。然后，我们提出了一种改进的方案，为单层和双层浅水模型提供更好的接触波分辨率。当对被动溶质解一个附加方程时，这种改进尤其明显。在这种情况下，原始方案不满足均匀分布示踪剂的c属性，而修改后的方案提供了精确到机器精度的解决方案。此外，改进后的方案更好地解决了接触不连续问题，其精度接近考虑完整波浪结构的全逆风非保守roe型方案。当达到更高的阶数时，各种方案之间的精度差异就不那么明显了。此外，本文还分析了二维格式在非零摩擦条件下的直线型和曲线型非平坦通道以及单层和双层方程下捕获稳态的能力。原始的一阶FORCE格式即使在粗糙的网格上也能正确地再现直线通道的纵剖面，但当通道有强烈的弯曲时，需要对该格式进行修改，否则需要非常精细的网格和非常高的精度，并且计算时间明显增加。
Recently, a non-conservative well-balanced FORCE-type scheme has been proposed for solving multidimensional non-conservative equations such as the shallow water equations [4], the two-fluid flow model of Pitman and Le and the two- and three-dimensional Baer–Nunziato equations for compressible multiphase flows [17]. In the present paper the original scheme is first rewritten in a suitable form that allows easy manipulation of numerical fluxes. We then propose a modified scheme that provides a better resolution of contact waves for both one-layer and two-layer shallow water models. The improvement is particularly evident when an additional equation is solved for a passive solute. In this case, the original scheme does not satisfy the C-property for a uniformly distribute tracer, whereas the modified scheme provides a solution that is exact up to machine precision. Moreover, the modified scheme better resolves contact discontinuities, with an accuracy close to the one provided by a fully-upwind non-conservative ROE-type scheme accounting for the complete wave structure. When higher orders are achieved, the difference in accuracy between the various schemes is less pronounced. Moreover, the capability of the two-dimensional scheme to capture steady states is analyzed for both straight and meandering non-flat channels with non-zero friction, and for both one-layer and two-layer equations. Whereas the original first order FORCE scheme is able to correctly reproduce the longitudinal profile in the case of a straight channel even on a coarse mesh, when the channel is strongly meandering a modification of the scheme is necessary, otherwise a very refined mesh and a very high order of accuracy are needed, with a notable increase of computational time.
影响因子：
4.1
作者：
Dumbser, Michael;Balsara, Dinshaw S.;Munz, Claus-Dieter
通讯作者：
Munz, Claus-Dieter