FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems

Dumbser, Michael; Hidalgo, Arturo; Castro, Manuel J.; Parés, Carlos; Toro, Eleuterio F.

doi:10.1016/j.cma.2009.10.016

Cited by 143 publications

(150 citation statements)

References 44 publications

Supporting

Mentioning

147

Contrasting

Order By: Relevance

“…An other possibility in approaching the matrix A i+1/2 is to use the technique proposed in [31,32,33]. In order to compute an approximation of the Roe linearization for the family of segments we should have…”

Section: Numerical Approach By Finite Volume Methodsmentioning

confidence: 99%

On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems

et al. 2014

View full text Add to dashboard Cite

In this paper we study Exner system and introduce a modified general definition for bedload transport flux. The new formulation has the advantage of taking into account the thickness of the sediment layer which avoids mass conservation problems in certain situations. Moreover, it reduces to a classical solid transport discharge formula in the case of quasi-uniform regime. We also present several numerical tests where we compare the proposed sediment transport formula with the classical formulation and we show the behaviour of the new model in different configurations.

show abstract

Section: Numerical Approach By Finite Volume Methodsmentioning

confidence: 99%

On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems

et al. 2014

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…The resulting PDE system is solved by a high order path-conservative WENO finite volume scheme on unstructured triangular meshes, to be applicable also in complex geometries. To assure low numerical dissipation at the free surface, which actually is crucial for the applications under consideration here, we use the new generalized Osher-type scheme of Dumbser and Toro [29], which resolves steady shear and contact waves exactly, in contrast to the simpler centered path-conservative FORCE schemes presented in [26].The model derives directly from first principles, namely the conservation of mass and momentum, hence it does not make any of the classical simplifications inherent in the commonly used shallow water models, which are based on depth-averaging, neglecting accelerations in gravity directions and on the resulting hydrostatic pressure distribution. We validate the new two-phase model against available analytical, numerical and experimental reference solutions and we also show some comparisons with the classical shallow water model for typical dambreak-type problems.…”

mentioning

confidence: 99%

A simple two-phase method for the simulation of complex free surface flows

Dumbser

2011

Computer Methods in Applied Mechanics and Engineering

Self Cite

View full text Add to dashboard Cite

“…In order to achieve high order of accuracy also in time we adopt the Lagrangian version of the local space-time discontinuous Galerkin method [9,10], first introduced for the Eulerian framework in [34,36,37,47]. The reconstructed polynomials w h (x, t n ) computed at the current time t n are evolved within one time step locally for each element T i (t) without requiring any neighbor information.…”

Section: Local Space-time Galerkin Predictor On Moving Unstructured Mmentioning

confidence: 99%

“…In [8][9][10][11]35] each lateral space-time sub-volume ∂C n i j has been mapped to a reference element ∂C E defined on a local reference system (χ 1 , χ 2 , τ ) and then parametrized with a set of bilinear (in 2D) or trilinear (in 3D) basis functions β k (χ 1 , χ 2 , τ ). The flux integral appearing in (37) has been computed on the reference element ∂C E using multidimensional Gaussian quadrature rules of suitable order of accuracy, see [76] for details. Since such a parametrization is not linear, the outward pointing normal vectorñ as well as the Jacobian of the transformation between ∂C n i j and ∂C E are not constant.…”

Section: Quadrature-free Finite Volume Scheme On Moving Meshesmentioning

confidence: 99%

An Efficient Quadrature-Free Formulation for High Order Arbitrary-Lagrangian–Eulerian ADER-WENO Finite Volume Schemes on Unstructured Meshes

Boscheri

Dumbser

2015

J Sci Comput

View full text Add to dashboard Cite

In this paper we present a new and efficient quadrature-free formulation for the family of cell-centered high order accurate direct arbitrary-Lagrangian-Eulerian one-step ADER-WENO finite volume schemes on unstructured triangular and tetrahedral meshes that has been developed by the authors in a recent series of papers (Boscheri et al. in J Comput ). High order of accuracy in time is obtained by using a local space-time Galerkin predictor on moving curved meshes, while a high order accurate nonlinear WENO method is adopted to produce high order essentially non-oscillatory reconstruction polynomials in space. The mesh is moved at each time step according to the solution of a node solver algorithm that assigns a unique velocity vector to each node of the mesh. A rezoning procedure can also be applied when mesh distortions and deformations become too severe. The space-time mesh is then constructed by straight edges connecting the vertex positions at the old time level t n with the new ones at the next time level t n+1 , yielding closed space-time control volumes, on the boundary of which the numerical flux must be integrated. This is done here with a new and efficient quadrature-free approach: the space-time boundaries are split into simplex sub-elements, i.e. either triangles in 2D or tetrahedra in 3D. This leads to space-time normal vectors as well as Jacobian matrices that are constant within each sub-element. Within the space-time Galerkin predictor stage that solves the Cauchy problem inside each element in the small, the discrete solution and the flux tensor are approximated using a nodal space-time basis. Since these space-time basis functions are defined on a reference element and do not change, their integrals over the simplex sub-surfaces of the space-time reference control volume can be integrated once and for all analytically during a preprocessing step. The resulting integrals are then used together B M. Dumbser 123 J Sci Comput with the space-time degrees of freedom of the predictor in order to compute the numerical flux that is needed in the finite volume scheme. We apply the high order algorithm presented in this paper to the equations of hydrodynamics obtaining convergence rates up to fourth order of accuracy in space and time. A set of classical Lagrangian test problems has been solved and the results have been compared with the ones given by the original formulation of the algorithm (Boscheri and Dumbser 2013, 2014). The efficiency has been monitored and measured for each test case and the new quadrature-free schemes were up to 3.7 times faster than the ones based on Gaussian quadrature.Keywords Arbitrary-Lagrangian-Eulerian (ALE) · Finite volume schemes · Quadraturefree flux integration · WENO reconstruction on moving unstructured meshes · High order of accuracy in space and time · Local rezoning · Hydrodynamics

show abstract

FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems

Cited by 143 publications

References 44 publications

On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems

On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems

A simple two-phase method for the simulation of complex free surface flows

An Efficient Quadrature-Free Formulation for High Order Arbitrary-Lagrangian–Eulerian ADER-WENO Finite Volume Schemes on Unstructured Meshes

Contact Info

Product

Resources

About