A Well-Balanced SPH-ALE Scheme for Shallow Water Applications

Prieto-Arranz, Alberto; Ramírez, Luis; Couceiro, Iván; Colominas, Ignasi; Nogueira, Xesús

doi:10.1007/s10915-021-01600-1

Cited by 4 publications

(5 citation statements)

References 61 publications

(118 reference statements)

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“…This test case has been proposed in Vazquez and Bermudez, 1994 52 and has been implemented in various forms in different models to test the lake at rest solution of shallow water equations. 53,54 The irregularity of the non erodible bed…”

Section: Scenario I: Lake At Rest With Irregular Bathymetrymentioning

confidence: 99%

“…This test‐case is presented to show the conservation properties of the system with respect to the presence of a still water surface in a domain with irregular bathymetry. This test case has been proposed in Vazquez and Bermudez, 1994 52 and has been implemented in various forms in different models to test the lake at rest solution of shallow water equations 53,54 . The irregularity of the non erodible bed

\left({z}_{\frac{1}{2}}\right)

makes it a suitable check for implementation of the source/sink terms within the numerical scheme.…”

Section: Model Testsmentioning

confidence: 99%

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Layered shallow water equations: Spatiotemporally varying layer ratios with specific adaptation to wet/dry interfaces

Bhat,

Pahar

2023

Numerical Methods in Fluids

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The study of multilayered shallow water equations has developed from a consideration of immiscible layers as a vertical mesh to the layer bounds as imaginary extremes for vertical integration of the flow equations. In the current work, a quasi three‐dimensional flow model has been developed with the consideration of the spatiotemporal flexibility/variability of the pervious vertical discretization/layer ratios. Thus, in principle, vertical layering offers a nonuniform grid with a temporal variation. The system of equations thus formulated comprises a conservative part and the appended source/sink terms. These source/sink terms pertain to the inter‐layer interactions such as mass/momenta transfer and interfacial stress, which have been treated in a novel implicit form alongwith the subgrid‐scale eddy‐viscosity for interlayer shear. They are integrated into the system through different physical considerations so as to arrive at a well‐balanced numerical scheme in a regular finite volume grid. The model has been validated through the standard test‐cases highlighting the conservation properties and the model's adaptability to uniform and nonuniform vertical meshes alongwith the spatiotemporal transitions of layer ratios, with a specific interest in limiting cases of wet/dry fronts. The increase in layer ratios tends to nearly replicate the full‐scale model results in experimental scenarios at a lesser computational overhead.

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Section: Scenario I: Lake At Rest With Irregular Bathymetrymentioning

confidence: 99%

\left({z}_{\frac{1}{2}}\right)

makes it a suitable check for implementation of the source/sink terms within the numerical scheme.…”

Section: Model Testsmentioning

confidence: 99%

Layered shallow water equations: Spatiotemporally varying layer ratios with specific adaptation to wet/dry interfaces

Bhat,

Pahar

2023

Numerical Methods in Fluids

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“…with κ s = n −1 the Strickler coefficient and n the Manning coefficient. An important aspect that should be noticed is that the hybrid FV/FE algorithm proposed is well balanced by construction so water at rest solutions are preserved [33,76,77].…”

Section: Shallow Water Equationsmentioning

confidence: 99%

A Massively Parallel Hybrid Finite Volume/Finite Element Scheme for Computational Fluid Dynamics

2021

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In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular for the approximate solution of the incompressible and compressible Navier-Stokes equations, as well as for the shallow water equations on staggered unstructured meshes in two and three space dimensions. The key features of the method are the use of an edge-based/face-based staggered dual mesh for the discretization of the nonlinear convective terms at the aid of explicit high resolution Godunov-type finite volume schemes, while pressure terms are discretized implicitly using classical continuous Lagrange finite elements on the primal simplex mesh. The resulting pressure system is symmetric positive definite and can thus be very efficiently solved at the aid of classical Krylov subspace methods, such as a matrix-free conjugate gradient method. For the compressible Navier-Stokes equations, the schemes are by construction asymptotic preserving in the low Mach number limit of the equations, hence a consistent hybrid FV/FE method for the incompressible equations is retrieved. All parts of the algorithm can be efficiently parallelized, i.e., the explicit finite volume step as well as the matrix-vector product in the implicit pressure solver. Concerning parallel implementation, we employ the Message-Passing Interface (MPI) standard in combination with spatial domain decomposition based on the free software package METIS. To show the versatility of the proposed schemes, we present a wide range of applications, starting from environmental and geophysical flows, such as dambreak problems and natural convection, over direct numerical simulations of turbulent incompressible flows to high Mach number compressible flows with shock waves. An excellent agreement with exact analytical, numerical or experimental reference solutions is achieved in all cases. Most of the simulations are run with millions of degrees of freedom on thousands of CPU cores. We show strong scaling results for the hybrid FV/FE scheme applied to the 3D incompressible Navier-Stokes equations, using millions of degrees of freedom and up to 4096 CPU cores. The largest simulation shown in this paper is the well-known 3D Taylor-Green vortex benchmark run on 671 million tetrahedral elements on 32,768 CPU cores, showing clearly the suitability of the presented algorithm for the solution of large CFD problems on modern massively parallel distributed memory supercomputers.

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“…[22][23][24] Despite their shortcomings, the Lagrange and Euler methods can be combined to leverage their advantages. For example, the arbitrary Lagrange-Euler (ALE) 25,26 method can combine the Lagrangian and Euler descriptions such that the cell nodes follow the material movement or remain fixed; this helps exploit and overcome the shortcoming of each method. Waltz et al 27 combined ALE with adaptive mesh refinement 28 to simulate an impact fluid problem on an unstructured grid.…”

Section: Introductionmentioning

confidence: 99%

A novel coupled Euler–Lagrange method for high resolution shock and discontinuities capturing

Jin,

Ning,

2023

Numerical Methods in Fluids

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The accurate capturing of shock waves by numerical methods has long been a focus of attention in engineering owing to singularity problems in discontinuities. In this article, a novel coupled Euler–Lagrange method (CELM) is proposed to capture shock waves and discontinuities with high resolution and high order of mapping accuracy. CELM arranges the Lagrange particles on an Euler grid to track the discontinuous points automatically, and the data pertaining to the grids and particles interact via a weighted mutual mapping method that not only achieves fourth‐order accuracy in a smooth area of the solution but also maintains a steep discontinuous transition in the discontinuous area. In the virtual particle method, virtual particles are derived from the existing real particles; thus, the inflow and outflow of the particles and interpolation accuracy of the boundary are more easily realized. An accuracy test and energy convergence test demonstrated the fourth‐order convergence accuracy and low energy dissipation of the CELM; the method exhibited lower error and better conservation ability than high‐precision schemes such as WENO3 and WENO5. The Sod shock tube problem and Woodward–Colella problem showed higher discontinuity resolution of the CELM and ability to accurately track discontinuity points. Examples of Riemann problems were employed to prove that the CELM exhibits lower dissipation and higher shock resolution than WENO3 and WENO5. The CELM also showed an accurate structure based on particle distribution. Shockwave diffraction tests were conducted to prove that the CELM results showed good agreement with the experimental data and exhibited an accurate expansion wave. The CELM can also accurately simulate the collision of an expansion wave and vortex.

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A Well-Balanced SPH-ALE Scheme for Shallow Water Applications

Cited by 4 publications

References 61 publications

Layered shallow water equations: Spatiotemporally varying layer ratios with specific adaptation to wet/dry interfaces

Layered shallow water equations: Spatiotemporally varying layer ratios with specific adaptation to wet/dry interfaces

A Massively Parallel Hybrid Finite Volume/Finite Element Scheme for Computational Fluid Dynamics

A novel coupled Euler–Lagrange method for high resolution shock and discontinuities capturing

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