An efficient unstructured MUSCL scheme for solving the 2D shallow water equations

Hou, Jingming; Liang, Qiuhua; Zhang, Hongbin; Hinkelmann, Reinhard

doi:10.1016/j.envsoft.2014.12.007

Cited by 98 publications

(59 citation statements)

References 96 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This test problem is widely used to verify well-balanced property of a numerical scheme towards moving steady state solution [7,8,25]. The moving steady-state water equilibrium is given by: …”

Section: Flow Over a Humpmentioning

confidence: 99%

“…Some of the popular methods of establishing second-order accuracy are Monotonic Upwind Scheme for Conservation Laws (MUSCL) scheme [1,[7][8][9], the Weighted Essentially Non-Oscillatory (WENO) scheme [10][11][12], and a high-resolution reconstruction procedure developed by [13] which has been widely employed for shallow water flows [5,14,15]. Reconstruction by MUSCL scheme may result in negative water depths at the interface which consequently give unphysical high velocities because of discharge divided by small water depths [16].…”

Section: Introductionmentioning

confidence: 99%

“…With appropriate numerical techniques, SWEs can model complex flows that involve sharp discontinuities and shocks. The most challenging issues in modeling shallow flows involve maintaining second-order accuracy, satisfying well-balanced condition, and avoiding numerical instabilities at wet-dry fronts [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

Rehman

Cho

2016

Water

View full text Add to dashboard Cite

This paper proposes a robust method for modeling shallow-water flows and near shore tsunami propagation, applicable for both simple and complex geometries with uneven beds. The novel aspect of the model includes the introduction of a new method for slope source terms treatment to preserve quiescent equilibrium over uneven topographies, applicable to both structured and unstructured mesh systems with equal accuracy. Our model is based on the Godunov-type finite volume numerical approximation. Second-order spatial and temporal accuracy is achieved through high resolution gradient reconstruction and the predictor-corrector method, respectively. The approximate Riemann solver of Harten, Lax, and van Leer with contact wave restoration (HLLC) is used to compute fluxes. Comparisons of the model's results with analytical, experimental, and published numerical solutions show that the proposed method is capable of accurately predicting experimental and real-time tsunami propagation/inundation, and dam-break flows over varying topographies.

show abstract

Section: Flow Over a Humpmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

Rehman

Cho

2016

Water

View full text Add to dashboard Cite

show abstract

“…Accurate and efficient solvers to model unsteady sediment transport problems have been demanded strongly by researchers and practitioners in fields such as river engineering (Parker 1979;Wu 2004) and coastal engineering (Butt and Russel 2000;Masselink and Russel 2006;Bakhtyar et al 2009). Many of these applications have been successfully addressed with two-dimensional (2D) shallow-water models coupled to bed-load and suspended-transport solvers (Begnudelli and Sanders 2006;Xia et al 2010;Soares-Frazao and Zech 2011;Hou et al 2015).…”

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Numerical Simulation of Bed-Load Transport of a Finite-Depth Sediment Layer: Applications to Channel Flushing

et al. 2017

View full text Add to dashboard Cite

Numerical modeling of bed-load transport in shallow flows, particularly oriented toward environmental flows, is an active field of research. Nevertheless, other possible applications exist. In particular, bed-load transport phenomena are relevant in urban drainage systems, including sewers. However, few applications of coupled two-dimensional (2D) shallow-water and bed-load transport models can be found, and their transfer from environmental applications-usually river and floodplain-into sewer applications requires some adaptation. Unlike to river systems, where there is a thick layer of sediment that constitutes a movable riverbed, sewer systems have thin layers of sediment that need to be removed, thus exposing a rigid, nonerodible surface. This problem requires careful numerical treatment to avoid generating errors and instability in the simulation. This paper deals with a numerical approach to tackle this issue in an efficient way that allows large-scale studies to be performed and provides empirical evidence that the proposed approach is accurate and applicable for sewage and channelflushing problems.

show abstract

“…Second group contains the methods on moving grids, which adapt so that a waterfront always coincides with a computational domain boundary. In flooding-drying problems the finite volume methods [9,10], finite element methods [11,12,13], finite difference methods [14,15], particle method [16] and others are used for the fluid flow modelling.…”

Section: Introductionmentioning

confidence: 99%

Numerical Modelling of Surface Waves in the Framework of the Shallow Water Model

Shokina¹,

Khakimzyanov²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

View full text Add to dashboard Cite

Abstract. An improved adaptive grid method is considered for the numerical solution of the problems on propagation and run-up of surface waves, described by the one-dimensional shallow water model. The modified algorithm for the realization of the explicit predictor-corrector scheme is presented, which is based on the new way of computation of the right-hand side of the shallow water equations. A new method for choosing the scheme parameters on the basis of the analysis of the differential approximation is suggested that guarantees the satisfaction of the TVD-property for the improved predictor-corrector scheme. The presented method for construction of different conservative schemes on moving grids is based on an appropriate choice of the scheme parameters for the predictor-corrector scheme, which represents the canonical form of the two-layer explicit schemes for the shallow water equations. The improved difference boundary conditions are obtained at the moving waterfront point using the known analytical solutions of the shallow water equations in the vicinity of a water-land boundary. These boundary conditions approximate the analytical solutions with a higher accuracy than the conditions used in the earlier works. The numerical results for the improved adaptive grid method are presented.

show abstract

An efficient unstructured MUSCL scheme for solving the 2D shallow water equations

Cited by 98 publications

References 96 publications

Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

Two-Dimensional Numerical Simulation of Bed-Load Transport of a Finite-Depth Sediment Layer: Applications to Channel Flushing

Numerical Modelling of Surface Waves in the Framework of the Shallow Water Model

Contact Info

Product

Resources

About