Adaptive moving mesh central-upwind schemes for hyperbolic system of PDEs: applications to compressible Euler equations and granular hydrodynamics

DOI10.1007/s42967-020-00082-6zbMath1499.65460OpenAlexW3081640947WikidataQ114216666 ScholiaQ114216666MaRDI QIDQ2077783

Zhuolin Qu, Tong Wu, Alexander Kurganov, Olga S. Rozanova

Publication date: 22 February 2022

Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s42967-020-00082-6

zbMATH Keywords

singular solutionsfinite-volume methodsgranular hydrodynamicscentral-upwind schemesEuler equations of gas dynamicsadaptive moving mesh methodsmoving mesh differential equations

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Finite volume methods applied to problems in fluid mechanics (76M12) Gas dynamics (general theory) (76N15) Hyperbolic conservation laws (35L65) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Granular flows (76T25) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Euler equations (35Q31)

Related Items (6)

Positivity-preserving and well-balanced adaptive surface reconstruction schemes for shallow water equations with wet-dry fronts ⋮ Well-balanced numerical method for atmospheric flow equations with gravity ⋮ Adaptive physical-constraints-preserving unstaggered central schemes for shallow water equations on quadrilateral meshes ⋮ A new S-M limiter entropy stable scheme based on moving mesh method for ideal MHD and SWMHD equations ⋮ One-dimensional/two-dimensional coupling approach with quadrilateral confluence region for modeling river systems ⋮ Well-balanced positivity preserving adaptive moving mesh central-upwind schemes for the Saint-Venant system

Uses Software

• HE-E1GODF
• GEOCLAW
• AMRCLAW

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A high-order moving mesh kinetic scheme based on WENO reconstruction for compressible flows on unstructured meshes
• Adaptive moving mesh methods
• On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes
• Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equations
• Adaptive mesh refinement for hyperbolic partial differential equations
• Adaptive grid generation from harmonic maps on Riemannian manifolds
• An adaptive grid method for two-dimensional viscous flows
• A unified moving grid gas-kinetic method in Eulerian space for viscous flow computation
• Hybrid Fourier-continuation method and weighted essentially non-oscillatory finite difference scheme for hyperbolic conservation laws in a single-domain framework
• Non-oscillatory central differencing for hyperbolic conservation laws
• On maximum-principle-satisfying high order schemes for scalar conservation laws
• Local adaptive mesh refinement for shock hydrodynamics
• An \(r\)-adaptive finite element method based upon moving mesh PDEs
• Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem
• A smoothness indicator for adaptive algorithms for hyperbolic systems
• A well-balanced positivity-preserving central-upwind scheme for shallow water equations on unstructured quadrilateral grids
• Well-balanced positivity preserving cell-vertex central-upwind scheme for shallow water flows
• Numerical approximation of hyperbolic systems of conservation laws
• Variational mesh adaptation. II: Error estimates and monitor functions
• New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• A robust moving mesh finite volume method applied to 1D hyperbolic conservation laws from magnetohydrodynamics
• Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh
• Strong Stability-Preserving High-Order Time Discretization Methods
• Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations
• Hybrid Compact-WENO Finite Difference Scheme with Conjugate Fourier Shock Detection Algorithm for Hyperbolic Conservation Laws
• Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
• Formation of singularities in solutions to ideal hydrodynamics of freely cooling inelastic gases
• Tsunami modelling with adaptively refined finite volume methods
• Pressure‐based adaption indicator for compressible euler equations
• Riemann Solvers and Numerical Methods for Fluid Dynamics
• Towards dense, realistic granular media in 2D
• High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
• Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems
• Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
• Finite Volume Methods for Hyperbolic Problems
• Accuracy of the Adaptive GRP Scheme and the Simulation of 2-D Riemann Problems for Compressible Euler Equations
• Numerical Entropy and Adaptivity for Finite Volume Schemes
• Central-upwind schemes on triangular grids for hyperbolic systems of conservation laws
• Kinetic Theory of Granular Gases
• Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers
• Generalized Riemann Problems in Computational Fluid Dynamics
• Formation of density singularities in ideal hydrodynamics of freely cooling inelastic gases: A family of exact solutions

This page was built for publication: Adaptive moving mesh central-upwind schemes for hyperbolic system of PDEs: applications to compressible Euler equations and granular hydrodynamics