High order ADER schemes for continuum mechanics
arXiv:1912.01964 · doi:10.3389/fphy.2020.00032
Abstract
In this paper we first review the development of high order ADER finite volume and ADER discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in 1999 by Toro et al. We show the modern variant of ADER based on a space-time predictor-corrector formulation in the context of ADER discontinuous Galerkin schemes with a posteriori subcell finite volume limiter on fixed and moving grids, as well as on space-time adaptive Cartesian AMR meshes. We then present and discuss the unified symmetric hyperbolic and thermodynamically compatible (SHTC) formulation of continuum mechanics developed by Godunov, Peshkov and Romenski (GPR model), which allows to describe fluid and solid mechanics in one single and unified first order hyperbolic system. In order to deal with free surface and moving boundary problems, a simple diffuse interface approach is employed, which is compatible with Eulerian schemes on fixed grids as well as direct Arbitrary-Lagrangian-Eulerian methods on moving meshes. We show some examples of moving boundary problems in fluid and solid mechanics.
References in corpus (40)
- E pur si muove: Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh
- A Posteriori Subcell Limiting of the Discontinuous Galerkin Finite Element Method for Hyperbolic Conservation Laws
- Very High Order $\PNM$ Schemes on Unstructured Meshes for the Resistive Relativistic MHD Equations
- ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement
- High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: viscous heat-conducting fluids and elastic solids
- Space-time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting
- Lagrangian ADER-WENO Finite Volume Schemes on Unstructured Tetrahedral Meshes for Conservative and Nonconservative Hyperbolic Systems in 3D
- A pressure-based semi-implicit space-time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier-Stokes equations at all Mach numbers
- High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes
- Adaptive Mesh Refinement for Hyperbolic Systems based on Third-Order Compact WENO Reconstruction
- Central WENO schemes for hyperbolic conservation laws on fixed and moving unstructured meshes
- CWENO: uniformly accurate reconstructions for balance laws
- High Order Space-Time Adaptive WENO Finite Volume Schemes for Non-Conservative Hyperbolic Systems
- Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes
- Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement
- Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes
- Continuum Mechanics and Thermodynamics in the Hamilton and the Godunov-type Formulations
- High order ADER schemes for a unified first order hyperbolic formulation of Newtonian continuum mechanics coupled with electro-dynamics
- Lagrangian ADER-WENO Finite Volume Schemes on Unstructured Triangular Meshes Based On Genuinely Multidimensional HLL Riemann Solvers
- High Order Lagrangian ADER-WENO Schemes on Unstructured Meshes - Application of Several Node Solvers to Hydrodynamics and Magnetohydrodynamics
- ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics
- Space-time adaptive ADER-DG schemes for dissipative flows: compressible Navier-Stokes and resistive MHD equations
- Efficient high order accurate staggered semi-implicit discontinuous Galerkin methods for natural convection problems
- Conformal and covariant Z4 formulation of the Einstein equations: strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes
- Well balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gasdynamics with gravity
- Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity
- Direct Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming unstructured meshes
- On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations
- High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension
- Arbitrary-Lagrangian-Eulerian ADER-WENO Finite Volume Schemes with Time-Accurate Local Time Stepping for Hyperbolic Conservation Laws
- A projection hybrid high order finite volume/finite element method for incompressible turbulent flows
- A multi-physics methodology for the simulation of the two-way interaction of reactive flow and elastoplastic structural response
- High Order Cell-Centered Lagrangian-Type Finite Volume Schemes with Time-Accurate Local Time Stepping on Unstructured Triangular Meshes
- Continuum mechanics with torsion
- Design and analysis of ADER-type schemes for model advection-diffusion-reaction equations
- A simple diffuse interface approach on adaptive Cartesian grids for the linear elastic wave equations with complex topography
- On the Eigenvalues of the ADER-WENO Galerkin Predictor
- A Numerical Scheme for Non-Newtonian Fluids and Plastic Solids under the GPR Model
- A unified Eulerian framework for multimaterial continuum mechanics
- A projection algorithm on the set of polynomials with two bounds
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- A structure-preserving staggered semi-implicit finite volume scheme for continuum mechanics
- High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension
- A semi-implicit hybrid finite volume / finite element scheme for all Mach number flows on staggered unstructured meshes
- Space-time adaptive ADER discontinuous Galerkin schemes for nonlinear hyperelasticity with material failure
- A unified first order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones
- On thermodynamically compatible finite volume schemes for continuum mechanics
- Simulation of non-Newtonian viscoplastic flows with a unified first order hyperbolic model and a structure-preserving semi-implicit scheme
- DeC and ADER: Similarities, Differences and a Unified Framework
- A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers
- Cellular Topology Optimization on Differentiable Voronoi Diagrams
- Modeling wavefields in saturated elastic porous media based on thermodynamically compatible system theory for multiphase mixtures
- A novel structure preserving semi-implicit finite volume method for viscous and resistive magnetohydrodynamics
- A new continuum model for general relativistic viscous heat-conducting media
- On Hamiltonian continuum mechanics
- An Arbitrary-Lagrangian-Eulerian hybrid finite volume/finite element method on moving unstructured meshes for the Navier-Stokes equations
- Efficient iterative arbitrary high order methods: an adaptive bridge between low and high order
- Two-derivative deferred correction time discretization for the discontinuous Galerkin method
- Unified description of fluids and solids in Smoothed Particle Hydrodynamics
- On improving the efficiency of ADER methods
- High-order ADER Discontinuous Galerkin schemes for a symmetric hyperbolic model of compressible barotropic two-fluid flows
- Analysis for Implicit and Implicit-Explicit ADER and DeC Methods for Ordinary Differential Equations, Advection-Diffusion and Advection-Dispersion Equations
- Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional detonation waves simulation
- High order well-balanced Arbitrary-Lagrangian-Eulerian ADER discontinuous Galerkin schemes on general polygonal moving meshes
- First-order hyperbolic formulation of the pure tetrad teleparallel gravity theory
- High-order discontinuous Galerkin schemes with subcell finite volume limiter and adaptive mesh refinement for a monolithic first-order BSSNOK formulation of the Einstein-Euler equations
- Semi-implicit hybrid finite volume/finite element method for the GPR model of continuum mechanics
- A cell-centered implicit-explicit Lagrangian scheme for a unified model of nonlinear continuum mechanics on unstructured meshes
- A staggered semi-implicit hybrid FV/FE projection method for weakly compressible flows