气候变化领域集成服务门户(CCPortal): A second-order numerical scheme for the porous shallow water equations based on a DOT ADER augmented Riemann solver

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DOI	10.1016/j.advwatres.2020.103587
	A second-order numerical scheme for the porous shallow water equations based on a DOT ADER augmented Riemann solver
	Ferrari A.; Vacondio R.; Mignosa P.
发表日期	2020
ISSN	0309-1708
卷号	140
英文摘要	In the present work, a novel DOT ADER numerical solver capable of handling porosity and bottom discontinuities in the framework of the 1D porous Shallow Water Equations (SWEs) is presented. In order to ensure the preservation of the water at rest condition, a new set of well-balanced governing equations based on the isotropic porosity parameter is derived. The effects exerted by the bed slope and porosity variation source terms are accurately accounted for inside the Riemann solver: to this purpose, an augmented Riemann problem is created by adding two fictitious equations stating the invariance of porosity and bottom in time to the SWEs system. With the aim of computing the non-conservative fluxes, which in the augmented system replace the original source terms, meanwhile ensuring robustness, stability and accuracy, a novel approximate numerical scheme, based on the entropy-satisfying DOT family, is introduced. The extension of the novel Riemann solver, which strictly conserves mass, to a second order of accuracy in both space and time is addressed in the ADER framework. The fulfillment of the C-property condition (i.e. the exact preservation of an initial quiescent flow) in the presence of a discontinuous porosity field and over a non-flat bottom with abrupt variation is theoretically proved and numerically verified. The capability of the proposed numerical scheme to simulate some Riemann problems developing across porosity discontinuities and bed steps is finally assessed. © 2020 Elsevier Ltd
关键词	Partial differential equations Porosity Augmented systems Governing equations Numerical scheme Numerical solvers Porosity variations Riemann problem Shallow water equation (SWEs)Shallow water equations Equations of motion discontinuity numerical model porosity shallow-water equation theoretical study
语种	英语
来源机构	Advances in Water Resources
文献类型	期刊论文
条目标识符	http://gcip.llas.ac.cn/handle/2XKMVOVA/131806
推荐引用方式 GB/T 7714	Ferrari A.,Vacondio R.,Mignosa P.. A second-order numerical scheme for the porous shallow water equations based on a DOT ADER augmented Riemann solver[J]. Advances in Water Resources,2020,140.
APA	Ferrari A.,Vacondio R.,&Mignosa P..(2020).A second-order numerical scheme for the porous shallow water equations based on a DOT ADER augmented Riemann solver.,140.
MLA	Ferrari A.,et al."A second-order numerical scheme for the porous shallow water equations based on a DOT ADER augmented Riemann solver".140(2020).