Overcoming numerical shockwave anomalies using energy balanced numerical schemes. Application to the shallow water equations with discontinuous topography
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Publication:1686466
DOI10.1016/j.jcp.2017.03.057zbMath1376.76034OpenAlexW2603119116MaRDI QIDQ1686466
Publication date: 15 December 2017
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: http://zaguan.unizar.es/record/70883
Finite volume methods applied to problems in fluid mechanics (76M12) Hyperbolic conservation laws (35L65)
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Uses Software
Cites Work
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- High order exactly well-balanced numerical methods for shallow water systems
- Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium
- Accurate numerical modeling of 1D flow in channels with arbitrary shape. Application of the energy balanced property
- Energy balanced numerical schemes with very high order. The augmented Roe flux ADER scheme. Application to the shallow water equations
- Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography
- A numerical study of postshock oscillations in slowly moving shock waves
- On postshock oscillations due to shock capturing schemes in unsteady flows
- The behavior of flux difference splitting schemes near slowly moving shock waves
- Weak solutions for partial differential equations with source terms: application to the shallow water equations
- Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magneto\-hydrodynamics
- Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux
- Approximate Riemann solvers, parameter vectors, and difference schemes
- Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry
- Restoration of the contact surface in the HLL-Riemann solver
- Upwind methods for hyperbolic conservation laws with source terms
- Computations of slowly moving shocks
- The numerical interface coupling of nonlinear hyperbolic systems of conservation laws. I: The scalar case
- On numerical treatment of the source terms in the shallow water equations
- On accuracy of adaptive grid methods for captured shocks
- Some approximate Godunov schemes to compute shallow-water equations with topography.
- The effects of numerical viscosities. I: Slowly moving shocks
- Efficiency and accuracy of lateralized HLL, HLLS and augmented Roe's scheme with energy balance for river flows in irregular channels
- Asymptotically and exactly energy balanced augmented flux-ADER schemes with application to hyperbolic conservation laws with geometric source terms
- Augmented versions of the HLL and HLLC Riemann solvers including source terms in one and two dimensions for shallow flow applications
- High-order well-balanced finite volume WENO schemes for shallow water equation with moving water
- A sign matrix based scheme for non-homogeneous PDE's with an analysis of the convergence stagnation phenomenon
- Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation
- Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry
- An analysis of the errors caused by using artificial viscosity terms to represent steady-state shock waves
- An evaluation of several differencing methods for inviscid fluid flow problems
- The Riemann problem for the one-dimensional, free-surface shallow water equations with a bed step: theoretical analysis and numerical simulations
- The influence of source terms on stability, accuracy and conservation in two-dimensional shallow flow simulation using triangular finite volumes
- Riemann Solvers and Numerical Methods for Fluid Dynamics
- On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
- Finite Volume Methods for Hyperbolic Problems
- A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations
- Flux difference splitting and the balancing of source terms and flux gradients
- Exact solutions to the Riemann problem of the shallow water equations with a bottom step
