A high-order finite volume method for systems of conservation laws-multi-dimensional optimal order detection (MOOD)

From MaRDI portal
Publication:544581

DOI10.1016/j.jcp.2011.02.026zbMath1218.65091OpenAlexW2088385269MaRDI QIDQ544581

Raphaël Loubère, Stéphane Clain, Steven Diot

Publication date: 15 June 2011

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2011.02.026




Related Items

A multi-resolution weighted compact nonlinear scheme for hyperbolic conservation lawsImproved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomialsA very high-order finite volume method for the time-dependent convection-diffusion problem with Butcher tableau extensionMulti-dimensional Optimal Order Detection (MOOD) — a Very High-Order Finite Volume Scheme for Conservation Laws on Unstructured MeshesAn admissibility and asymptotic-preserving scheme for systems of conservation laws with source term on 2D unstructured meshesA Priori Subcell Limiting Approach for the FR/CPR Method on Unstructured MeshesSelf-adjusting steepness-based schemes that preserve discontinuous structures in compressible flowsMulti-material swept face remapping on polyhedral meshesExaHyPE: an engine for parallel dynamically adaptive simulations of wave problemsThermodynamically compatible discretization of a compressible two-fluid model with two entropy inequalitiesUnnamed ItemA modified a posteriori subcell limiter for high order flux reconstruction scheme for one-dimensional detonation simulationApplications of limiters, neural networks and polynomial annihilation in higher-order FD/FV schemesTotal of time variation diminishing principle for conservation laws``\textit{A posteriori} limited high order and robust schemes for transient simulations of fluid flows in gas dynamicsA posteriori stabilized sixth-order finite volume scheme with adaptive stencil construction: basics for the 1D steady-state hyperbolic equationsOn the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutionsStencil selection algorithms for WENO schemes on unstructured meshesAdmissibility preserving subcell limiter for Lax-Wendroff flux reconstructionRealizable second-order finite-volume schemes for the advection of moment sets of the particle size distributionEfficient methods with higher order interpolation and MOOD strategy for compressible turbulence simulationsOn the partition noise in chosen particle weighted methods and its consequences for weakly-compressible flow modelsA Reinforcement Learning Based Slope Limiter for Two-Dimensional Finite Volume SchemesA Posteriori Local Subcell Correction of High-Order Discontinuous Galerkin Scheme for Conservation Laws on Two-Dimensional Unstructured GridsPositivity-preserving CE/SE schemes for solving the compressible Euler and Navier-Stokes equations on hybrid unstructured meshesGlobal entropy stability for a class of unlimited second-order schemes for 2D hyperbolic systems of conservation laws on unstructured meshesTriangular metric-based mesh adaptation for compressible multi-material flows in semi-Lagrangian coordinatesA positivity-preserving adaptive-order finite-difference scheme for GRMHDAn almost fail-safe a-posteriori limited high-order CAT schemeRecasting an operator splitting solver into a standard finite volume flux-based algorithm. The case of a Lagrange-projection-type method for gas dynamicsA combination of residual distribution and the active flux formulations or a new class of schemes that can combine several writings of the same hyperbolic problem: application to the 1D Euler equationsA unified framework for non-linear reconstruction schemes in a compact stencil. I: Beyond second orderA new mean preserving moving least squares method for arbitrary order finite volume schemesA MOOD-like compact high order finite volume scheme with adaptive mesh refinement\texttt{UCNS3D}: an open-source high-order finite-volume unstructured CFD solverA diffuse interface method for complex three-dimensional free surface flowsA sixth-order finite volume method for multidomain convection-diffusion problem with discontinuous coefficientsA Multi-Dimensional Shock-Capturing Limiter for High-Order Least Square-Based Finite Difference-Finite Volume Method on Unstructured GridsDesigning Several Types of Oscillation-Less and High-Resolution Hybrid Schemes on Block-Structured GridsCentral WENO Subcell Finite Volume Limiters for ADER Discontinuous Galerkin Schemes on Fixed and Moving Unstructured MeshesA Study of Several Artificial Viscosity Models within the Discontinuous Galerkin FrameworkA Decoupled and Positivity-Preserving DDFVS cheme for Diffusion Problems on Polyhedral MeshesA High-Order Cell-Centered Discontinuous Galerkin Multi-Material Arbitrary Lagrangian-Eulerian MethodA Higher Order Interpolation Scheme of Finite Volume Method for Compressible Flow on Curvilinear GridsAn a posteriori-implicit turbulent model with automatic dissipation adjustment for large eddy simulation of compressible flowsStencil selection algorithms for WENO schemes on unstructured meshesAn unconditionally stable staggered pressure correction scheme for the compressible Navier-Stokes equationsEfficient implementation of ADER discontinuous Galerkin schemes for a scalable hyperbolic PDE engineAn admissibility and asymptotic preserving scheme for systems of conservation laws with source term on 2D unstructured meshes with high-order MOOD reconstructionWENO schemes on unstructured meshes using a relaxed \textit{a posteriori} MOOD limiting approachHigh-accurate SPH method with multidimensional optimal order detection limitingA computationally efficient ductile damage model accounting for nucleation and micro-inertia at high triaxialitiesAn \textit{a posteriori}, efficient, high-spectral resolution hybrid finite-difference method for compressible flowsStationary Discrete Shock Profiles for Scalar Conservation Laws with a Discontinuous Galerkin MethodCompact approximate Taylor methods for systems of conservation lawsMicrotubules (MT) a key target in oncology: mathematical modeling of anti-MT agents on cell migrationA computational realization of a semi-Lagrangian method for solving the advection equationOn High-Precision $$L^\infty $$-stable IMEX Schemes for Scalar Hyperbolic Multi-scale EquationsWeno Scheme for Transport Equation on Unstructured Grids with a DDFV ApproachA Gradient Compression-Based Compact High-Order Gas-Kinetic Scheme on 3D Hybrid Unstructured MeshesThe p-Weighted Limiter for the Discontinuous Galerkin Method in Solving Compressible Flows on Tetrahedral GridsA staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbersA MUSCL-type segregated -- explicit staggered scheme for the Euler equationsA posteriori sub-cell finite volume limiting of staggered semi-implicit discontinuous Galerkin schemes for the shallow water equationsHigh order direct arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changesA staggered semi-implicit hybrid FV/FE projection method for weakly compressible flowsSpace-time adaptive ADER discontinuous Galerkin schemes for nonlinear hyperelasticity with material failureArbitrary high-order non-oscillatory scheme on hybrid unstructured grids based on multi-moment finite volume methodA reduced-dissipation WENO scheme with automatic dissipation adjustmentAn \textit{a posteriori} strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equationsHigh order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tensionA single-step third-order temporal discretization with Jacobian-free and Hessian-free formulations for finite difference methodsAn efficient quadrature-free formulation for high order arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes on unstructured meshes\textit{A posteriori} finite-volume local subcell correction of high-order discontinuous Galerkin schemes for the nonlinear shallow-water equationsA high-order compact limiter based on spatially weighted projections for the spectral volume and the spectral differences methodA coupled discontinuous Galerkin-finite volume framework for solving gas dynamics over embedded geometriesFinite element formulation for compressible multiphase flows and its application to pyroclastic gravity currentsImplicit finite volume method with a posteriori limiting for transport networksA 3D cell-centered ADER MOOD finite volume method for solving updated Lagrangian hyperelasticity on unstructured gridsHigh-order Scharfetter-Gummel-based schemes and applications to gas discharge modelingA high order special relativistic hydrodynamic and magnetohydrodynamic code with space-time adaptive mesh refinement\textit{A posteriori} stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equationsExtended bounds limiter for high-order finite-volume schemes on unstructured meshesHigher-order multi-dimensional limiting strategy for discontinuous Galerkin methods in compressible inviscid and viscous flowsSpace-time adaptive ADER discontinuous Galerkin finite element schemes with \textit{a posteriori} sub-cell finite volume limitingHigh order accurate conservative remapping scheme on polygonal meshes using \textit{a posteriori} MOOD limitingThe MOOD method for the non-conservative shallow-water systemA new paradigm of dissipation-adjustable, multi-scale resolving schemes for compressible flowsADER-WENO finite volume schemes with space-time adaptive mesh refinementTowards an ultra efficient kinetic scheme. II: The high order caseLagrangian ADER-WENO finite volume schemes on unstructured triangular meshes based on genuinely multidimensional HLL Riemann solversTVD-MOOD schemes based on implicit-explicit time integrationA direct arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D\textit{A posteriori} subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation lawsHigh order cell-centered Lagrangian-type finite volume schemes with time-accurate local time stepping on unstructured triangular meshesDirect arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation lawsHybrid spectral difference/embedded finite volume method for conservation lawsA staggered semi-implicit discontinuous Galerkin scheme with a posteriori subcell finite volume limiter for the Euler equations of gasdynamicsConstructing higher order discontinuity-capturing schemes with upwind-biased interpolations and boundary variation diminishing algorithmAn efficient class of WENO schemes with adaptive orderA simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer-Nunziato modelA well-balanced scheme for the shallow-water equations with topography or Manning frictionSimple a posteriori slope limiter (post limiter) for high resolution and efficient flow computationsA 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 numbersPositivity-preserving method for high-order conservative schemes solving compressible Euler equationsA high-order flux reconstruction method for 3D mixed overset meshesSolution property preserving reconstruction BVD+MOOD scheme for compressible Euler equations with source terms and detonationsArbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshesA second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamicsAdaptive-mesh-refinement for hyperbolic systems of conservation laws based on a posteriori stabilized high order polynomial reconstructionsInverse Lax-Wendroff boundary treatment for compressible Lagrange-remap hydrodynamics on Cartesian gridsA simple extended compact nonlinear scheme with adaptive dissipation controlNew directional vector limiters for discontinuous Galerkin methodsA simple diffuse interface approach on adaptive Cartesian grids for the linear elastic wave equations with complex topographyA fifth-order shock capturing scheme with two-stage boundary variation diminishing algorithm\textit{A posteriori} correction of high-order discontinuous Galerkin scheme through subcell finite volume formulation and flux reconstructionTheoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticityAn efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemesHigh order direct arbitrary-Lagrangian-Eulerian (ALE) \(P_NP_M\) schemes with WENO adaptive-order reconstruction on unstructured meshesA conservative solver for surface-tension-driven multiphase flows on collocated unstructured gridsA moment limiter for the discontinuous Galerkin method on unstructured tetrahedral meshesAn alternative SPH formulation: ADER-WENO-SPHA semi-implicit hybrid finite volume/finite element scheme for all Mach number flows on staggered unstructured meshesArbitrary high order central non-oscillatory schemes on mixed-element unstructured meshesPositivity preserving and entropy consistent approximate Riemann solvers dedicated to the high-order MOOD-based finite volume discretization of Lagrangian and Eulerian gas dynamicsAn extended seventh-order compact nonlinear scheme with positivity-preserving propertyA two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning frictionA well-balanced scheme for the shallow-water equations with topographySecond-order implicit-explicit total variation diminishing schemes for the Euler system in the low Mach regimeA priori neural networks versus a posteriori MOOD loop: a high accurate 1D FV scheme testing bedA local time stepping method for thermal energy transport in district heating networksHybrid central-upwind finite volume schemes for solving the Euler and Navier-Stokes equationsEfficient implementation of high order unstructured WENO schemes for cavitating flowsHigh-order unstructured Lagrangian one-step WENO finite volume schemes for non-conservative hyperbolic systems: applications to compressible multi-phase flowsA high order positivity-preserving conservative WENO remapping method on 2D quadrilateral meshesA posteriori limiting for 2D Lagrange plus remap schemes solving the hydrodynamics system of equationsA posteriori subcell finite volume limiter for general \(P_NP_M\) schemes: applications from gasdynamics to relativistic magnetohydrodynamicsHybrid finite volume weighted essentially non-oscillatory schemes with linear central reconstructionsHigh order direct arbitrary-Lagrangian-Eulerian (ALE) finite volume schemes for hyperbolic systems on unstructured meshesHigher-order finite volume differential operators with selective upwinding on the icosahedral spherical gridA simple robust and accurate \textit{a posteriori} sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshesA MOOD-MUSCL hybrid formulation for the non-conservative shallow-water systemA sixth-order finite volume method for diffusion problem with curved boundariesHigh order space-time adaptive ADER-WENO finite volume schemes for non-conservative hyperbolic systemsOn thermodynamically compatible finite volume methods and path-conservative ADER discontinuous Galerkin schemes for turbulent shallow water flowsA well-balanced SPH-ALE scheme for shallow water applicationsA sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulationAssessment of a non-conservative four-equation multiphase system with phase transitionAn arbitrary high order well-balanced ADER-DG numerical scheme for the multilayer shallow-water model with variable densityMOODHigh order modal discontinuous Galerkin implicit-explicit Runge Kutta and linear multistep schemes for the Boltzmann model on general polygonal meshesDouble distribution function-based discrete gas kinetic scheme for viscous incompressible and compressible flowsA Hermite WENO scheme with artificial linear weights for hyperbolic conservation lawsA first order hyperbolic reformulation of the Navier-Stokes-Korteweg system based on the GPR model and an augmented Lagrangian approachCompact multi-stage reconstruction method on polyhedral unstructured grids: extension to higher-order finite volume schemeGP-MOOD: a positivity-preserving high-order finite volume method for hyperbolic conservation lawsA relaxed \textit{a posteriori} MOOD algorithm for multicomponent compressible flows using high-order finite-volume methods on unstructured meshesShifted boundary polynomial corrections for compressible flows: high order on curved domains using linear meshesA cell-centered discontinuous Galerkin multi-material arbitrary Lagrangian-Eulerian method in axisymmetric geometryHybrid discontinuous Galerkin-finite volume techniques for compressible flows on unstructured meshesA new 3D OpenFoam solver with improved resolution for hyperbolic systems on hybrid unstructured grids



Cites Work