Journal of Computational Physics, ISSN 0021-9991, 11/2014, Volume 276, pp. 252 - 290

Finite volume methods traditionally employ dimension by dimension extension of the one-dimensional reconstruction and averaging procedures to achieve spatial...

Finite volume method | Rotational invariance | Isotropic discretization | NUMERICAL-METHODS | APPROXIMATIONS | DIFFERENCE SCHEMES | ALGORITHMS | SIMULATION | PHYSICS, MATHEMATICAL | ANISOTROPY | HIGH-ORDER SCHEMES | WAVE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ADVECTION | FLOWS | Anisotropy | Differential equations | Force and energy | Reconstruction | Discretization | Mathematical analysis | Truncation errors | Derivatives | Kinetic energy | Three dimensional

Finite volume method | Rotational invariance | Isotropic discretization | NUMERICAL-METHODS | APPROXIMATIONS | DIFFERENCE SCHEMES | ALGORITHMS | SIMULATION | PHYSICS, MATHEMATICAL | ANISOTROPY | HIGH-ORDER SCHEMES | WAVE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ADVECTION | FLOWS | Anisotropy | Differential equations | Force and energy | Reconstruction | Discretization | Mathematical analysis | Truncation errors | Derivatives | Kinetic energy | Three dimensional

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 05/2016, Volume 106, Issue 8, pp. 593 - 622

Summary A family of fourth‐order coupled implicit–explicit time schemes is presented as a special case of fourth‐order coupled implicit schemes for linear wave...

wave equations | consistency analysis | high‐order numerical methods | locally implicit schemes | time discretization | Time discretization | Consistency analysis | High-order numerical methods | Locally implicit schemes | Wave equations | Numerical analysis | Computer simulation | Discretization | Mathematical analysis | Joining | Mathematical models | Dispersions | Analysis of PDEs | Mathematics

wave equations | consistency analysis | high‐order numerical methods | locally implicit schemes | time discretization | Time discretization | Consistency analysis | High-order numerical methods | Locally implicit schemes | Wave equations | Numerical analysis | Computer simulation | Discretization | Mathematical analysis | Joining | Mathematical models | Dispersions | Analysis of PDEs | Mathematics

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2014, Volume 52, Issue 6, pp. 2676 - 2702

We construct quasi–Monte Carlo methods to approximate the expected values of linear functionals of Petrov–Galerkin discretizations of parametric operator...

Integers | Approximation | Integrands | Function spaces | Numerical integration | Mathematical lattices | Error bounds | Polynomials | Mathematical vectors | Sobolev spaces | Petrov-Galerkin discretization | Interlaced polynomial lattice rules | Parametric operator equations | Infinite dimensional quadrature | Quasi-Monte Carlo methods | Higher order digital nets | HILBERT-SPACES | MATHEMATICS, APPLIED | SMOOTH FUNCTIONS | quasi-Monte Carlo methods | interlaced polynomial lattice rules | ALGORITHMS | higher order digital nets | MULTIVARIATE INTEGRATION | POLYNOMIAL LATTICE RULES | PARTIAL-DIFFERENTIAL-EQUATIONS | parametric operator equations | ARBITRARY HIGH-ORDER | COEFFICIENTS | EFFICIENT | infinite dimensional quadrature | BY-COMPONENT CONSTRUCTION | Operators | Construction | Discretization | Mathematical analysis | Fluctuation | Lattices | Mathematical models | Convergence

Integers | Approximation | Integrands | Function spaces | Numerical integration | Mathematical lattices | Error bounds | Polynomials | Mathematical vectors | Sobolev spaces | Petrov-Galerkin discretization | Interlaced polynomial lattice rules | Parametric operator equations | Infinite dimensional quadrature | Quasi-Monte Carlo methods | Higher order digital nets | HILBERT-SPACES | MATHEMATICS, APPLIED | SMOOTH FUNCTIONS | quasi-Monte Carlo methods | interlaced polynomial lattice rules | ALGORITHMS | higher order digital nets | MULTIVARIATE INTEGRATION | POLYNOMIAL LATTICE RULES | PARTIAL-DIFFERENTIAL-EQUATIONS | parametric operator equations | ARBITRARY HIGH-ORDER | COEFFICIENTS | EFFICIENT | infinite dimensional quadrature | BY-COMPONENT CONSTRUCTION | Operators | Construction | Discretization | Mathematical analysis | Fluctuation | Lattices | Mathematical models | Convergence

Journal Article

SIAM Review, ISSN 0036-1445, 3/2001, Volume 43, Issue 1, pp. 89 - 112

In this paper we review and further develop a class of strong stability-preserving (SSP) high-order time discretizations for semidiscrete method of lines...

Conservation laws | Approximation | Eulers method | Applied mathematics | Odes | Mathematics | Entropy | Problems and Techniques | Grants | Runge Kutta method | Coefficients | Strong stability preserving | Time discretization | Runge-Kutta methods | High-order accuracy | Multistep methods | MATHEMATICS, APPLIED | RUNGE-KUTTA SCHEMES | HIGH-RESOLUTION SCHEMES | APPROXIMATIONS | time discretization | multistep methods | high-order accuracy | strong stability preserving | HYPERBOLIC CONSERVATION-LAWS | FINITE-ELEMENT METHOD | Differential equations | Research

Conservation laws | Approximation | Eulers method | Applied mathematics | Odes | Mathematics | Entropy | Problems and Techniques | Grants | Runge Kutta method | Coefficients | Strong stability preserving | Time discretization | Runge-Kutta methods | High-order accuracy | Multistep methods | MATHEMATICS, APPLIED | RUNGE-KUTTA SCHEMES | HIGH-RESOLUTION SCHEMES | APPROXIMATIONS | time discretization | multistep methods | high-order accuracy | strong stability preserving | HYPERBOLIC CONSERVATION-LAWS | FINITE-ELEMENT METHOD | Differential equations | Research

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 03/2018, Volume 356, pp. 410 - 438

We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we...

Simultaneous approximation terms | Summation-by-parts | Nonlinear entropy stability | High-order discretizations | Curved elements | Unstructured grid | General elements | NONLINEAR CONSERVATION-LAWS | FINITE-DIFFERENCE SCHEMES | BOUNDARY-CONDITIONS | FORM | COMPUTATIONS | PHYSICS, MATHEMATICAL | COMPRESSIBLE EULER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SYSTEMS | OPERATORS

Simultaneous approximation terms | Summation-by-parts | Nonlinear entropy stability | High-order discretizations | Curved elements | Unstructured grid | General elements | NONLINEAR CONSERVATION-LAWS | FINITE-DIFFERENCE SCHEMES | BOUNDARY-CONDITIONS | FORM | COMPUTATIONS | PHYSICS, MATHEMATICAL | COMPRESSIBLE EULER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SYSTEMS | OPERATORS

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 3/2009, Volume 38, Issue 3, pp. 251 - 289

Strong stability preserving (SSP) high order time discretizations were developed to ensure nonlinear stability properties necessary in the numerical solution...

Spectral deferred correction methods | Computational Mathematics and Numerical Analysis | Algorithms | Runge–Kutta methods | Multistep methods | Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | High order accuracy | Strong stability preserving | Mathematics | Time discretization | Runge-Kutta methods | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | LOW-STORAGE | ABSOLUTE MONOTONICITY | CONTRACTIVITY | RUNGE-KUTTA SCHEMES | NUMERICAL-SOLUTION | HIGH-RESOLUTION SCHEMES | DISCONTINUOUS GALERKIN METHODS | CONSERVATION-LAWS | GENERAL MONOTONICITY | Universities and colleges | Stability | Discretization | Preserves | Norms | Nonlinearity | Mathematical models | Spectra | Preserving

Spectral deferred correction methods | Computational Mathematics and Numerical Analysis | Algorithms | Runge–Kutta methods | Multistep methods | Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | High order accuracy | Strong stability preserving | Mathematics | Time discretization | Runge-Kutta methods | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | LOW-STORAGE | ABSOLUTE MONOTONICITY | CONTRACTIVITY | RUNGE-KUTTA SCHEMES | NUMERICAL-SOLUTION | HIGH-RESOLUTION SCHEMES | DISCONTINUOUS GALERKIN METHODS | CONSERVATION-LAWS | GENERAL MONOTONICITY | Universities and colleges | Stability | Discretization | Preserves | Norms | Nonlinearity | Mathematical models | Spectra | Preserving

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2015, Volume 283, pp. 329 - 359

A robust and high order accurate Residual Distribution (RD) scheme for the discretization of the steady Navier–Stokes equations is presented. The proposed...

Unstructured meshes | Gradient reconstruction | High order schemes | Navier–Stokes equations | Residual distribution | Compressible flows | Navier-Stokes equations | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | KRYLOV METHODS | UPWIND SCHEME | CONSTRUCTION | COMPUTATION | EULER | Fluid dynamics | Finite element method | Discretization | Mathematical analysis | Flux | Nonlinearity | Mathematical models | Continuity | Standards

Unstructured meshes | Gradient reconstruction | High order schemes | Navier–Stokes equations | Residual distribution | Compressible flows | Navier-Stokes equations | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | KRYLOV METHODS | UPWIND SCHEME | CONSTRUCTION | COMPUTATION | EULER | Fluid dynamics | Finite element method | Discretization | Mathematical analysis | Flux | Nonlinearity | Mathematical models | Continuity | Standards

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 11/2015, Volume 79, Issue 9, pp. 437 - 455

Summary This paper investigates some important numerical aspects for the simulation of model rocket combustors. Precisely, (1) a new high‐order discretization...

rocket combustion | coaxial injector | turbulence | URANS | high‐order discretization | MLP, multi‐dimensional limiting process | Coaxial injector | Turbulence | Rocket combustion | High-order discretization | MLP, multi-dimensional limiting process | FLAMES | HIGH-PRESSURE | IMPLICIT MULTIGRID METHOD | PHYSICS, FLUIDS & PLASMAS | FINITE-RATE CHEMISTRY | PART II | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | high-order discretization | MULTIDIMENSIONAL LIMITING PROCESS | FLOWS | SCHEMES | Rockets | Axisymmetric | Computer simulation | Discretization | Mathematical models | Fluxes | Walls | Navier-Stokes equations

rocket combustion | coaxial injector | turbulence | URANS | high‐order discretization | MLP, multi‐dimensional limiting process | Coaxial injector | Turbulence | Rocket combustion | High-order discretization | MLP, multi-dimensional limiting process | FLAMES | HIGH-PRESSURE | IMPLICIT MULTIGRID METHOD | PHYSICS, FLUIDS & PLASMAS | FINITE-RATE CHEMISTRY | PART II | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | high-order discretization | MULTIDIMENSIONAL LIMITING PROCESS | FLOWS | SCHEMES | Rockets | Axisymmetric | Computer simulation | Discretization | Mathematical models | Fluxes | Walls | Navier-Stokes equations

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 08/2019, Volume 390, pp. 175 - 202

We present an efficient nodal discontinuous Galerkin method for approximating nearly incompressible flows using the Boltzmann equations. The equations are...

Discontinuous Galerkin | Boltzmann equation | Perfectly matching layer | Semi-analytic | GPU | Multirate | HIGH-ORDER | COMPUTATIONS | MODEL | SIMULATION | PHYSICS, MATHEMATICAL | RUNGE-KUTTA SCHEMES | ELEMENT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PERFECTLY MATCHED LAYER | CONSTRUCTION | EULER | Environmental law | Boundary layer | Viscosity | Nonlinear equations | Computational fluid dynamics | Fluid flow | Variations | Incompressible flow | Flow equations | Discretization | Mathematical analysis | Galerkin method | Hermite polynomials | Matching layers (electronics) | Boundary layers | Cylinders

Discontinuous Galerkin | Boltzmann equation | Perfectly matching layer | Semi-analytic | GPU | Multirate | HIGH-ORDER | COMPUTATIONS | MODEL | SIMULATION | PHYSICS, MATHEMATICAL | RUNGE-KUTTA SCHEMES | ELEMENT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PERFECTLY MATCHED LAYER | CONSTRUCTION | EULER | Environmental law | Boundary layer | Viscosity | Nonlinear equations | Computational fluid dynamics | Fluid flow | Variations | Incompressible flow | Flow equations | Discretization | Mathematical analysis | Galerkin method | Hermite polynomials | Matching layers (electronics) | Boundary layers | Cylinders

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2018, Volume 372, pp. 616 - 639

We present a novel hyperviscosity formulation for stabilizing RBF-FD discretizations of the advection–diffusion equation. The amount of hyperviscosity is...

Radial basis function | Hyperviscosity | High-order method | Advection–diffusion | Meshfree | NONLINEAR CONSERVATION-LAWS | APPROXIMATIONS | SPHERE | ALGORITHM | INTERPOLANTS | PHYSICS, MATHEMATICAL | POLYNOMIALS | SPECTRAL VISCOSITY METHOD | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Advection-diffusion | STABLE COMPUTATIONS | SURFACES | advection-diffusion | meshfree | high-order method | hyperviscosity

Radial basis function | Hyperviscosity | High-order method | Advection–diffusion | Meshfree | NONLINEAR CONSERVATION-LAWS | APPROXIMATIONS | SPHERE | ALGORITHM | INTERPOLANTS | PHYSICS, MATHEMATICAL | POLYNOMIALS | SPECTRAL VISCOSITY METHOD | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Advection-diffusion | STABLE COMPUTATIONS | SURFACES | advection-diffusion | meshfree | high-order method | hyperviscosity

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 02/2018, Volume 86, Issue 6, pp. 392 - 413

Summary In this paper, a central essentially non‐oscillatory approximation based on a quadratic polynomial reconstruction is considered for solving the...

error estimation | mesh adaptation | finite volume | Euler flow | compressible flow | hyperbolic | VISCOUS FLOWS | PHYSICS, FLUIDS & PLASMAS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | INTERPOLATION ERROR | OPTIMIZATION | GENERATION | Anisotropy | Analysis | Adaptations | Reconstruction | Approximation | Error analysis | Methodology | Acoustic propagation | Euler-Lagrange equation | Equations | Optimization | Discretization | Mathematical analysis | Polynomials | Mathematical models | Analysis of PDEs | Mathematics | Optimization and Control

error estimation | mesh adaptation | finite volume | Euler flow | compressible flow | hyperbolic | VISCOUS FLOWS | PHYSICS, FLUIDS & PLASMAS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | INTERPOLATION ERROR | OPTIMIZATION | GENERATION | Anisotropy | Analysis | Adaptations | Reconstruction | Approximation | Error analysis | Methodology | Acoustic propagation | Euler-Lagrange equation | Equations | Optimization | Discretization | Mathematical analysis | Polynomials | Mathematical models | Analysis of PDEs | Mathematics | Optimization and Control

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2020, Volume 402, Issue C, p. 109047

•High-order accurate wave equation scattering solver from smooth surfaces.•Retarded potential Volterra integral equation time-stepped...

High-order methods | Time-domain integral equations | Acoustic scattering | DECAY | APPROXIMATIONS | ALGORITHM | SMOOTH | PHYSICS, MATHEMATICAL | TRANSIENT ELECTROMAGNETIC SCATTERING | MULTISTEP | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | QUADRATURE | WAVE-EQUATION | Predictor-corrector methods | Toruses | Algorithms | Convolution | Discretization | Integral equations | Scattering | Time domain analysis | Quadratures

High-order methods | Time-domain integral equations | Acoustic scattering | DECAY | APPROXIMATIONS | ALGORITHM | SMOOTH | PHYSICS, MATHEMATICAL | TRANSIENT ELECTROMAGNETIC SCATTERING | MULTISTEP | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | QUADRATURE | WAVE-EQUATION | Predictor-corrector methods | Toruses | Algorithms | Convolution | Discretization | Integral equations | Scattering | Time domain analysis | Quadratures

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 09/2016, Volume 303, pp. 171 - 188

We introduce different high order time discretization schemes for backward semi-Lagrangian methods. These schemes are based on multi-step schemes like...

High order time discretization | Guiding-centre model | Plasma physics | Semi-Lagrangian scheme | Vlasov–Poisson model | Vlasov-Poisson model | VLASOV | MATHEMATICS, APPLIED | BEAMS | CODE | DISCONTINUOUS GALERKIN METHODS | CONVERGENCE | TURBULENCE | NUMERICAL-SIMULATION | SCHEMES | Methods | Numerical analysis | Analysis | Permissible error | Computer simulation | Discretization | Transport equations | Mathematical analysis | Strategy | Mathematical models | Finite difference method | Numerical Analysis | Mathematics

High order time discretization | Guiding-centre model | Plasma physics | Semi-Lagrangian scheme | Vlasov–Poisson model | Vlasov-Poisson model | VLASOV | MATHEMATICS, APPLIED | BEAMS | CODE | DISCONTINUOUS GALERKIN METHODS | CONVERGENCE | TURBULENCE | NUMERICAL-SIMULATION | SCHEMES | Methods | Numerical analysis | Analysis | Permissible error | Computer simulation | Discretization | Transport equations | Mathematical analysis | Strategy | Mathematical models | Finite difference method | Numerical Analysis | Mathematics

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2016, Volume 38, Issue 3, pp. A1770 - A1787

We present a fast direct solver for two-dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We...

Adaptivity | High-order accuracy | Electromagnetic scattering | Acoustic scattering | Penetrable media | Fast direct solver | Integral equation | Lippmann-schwinger equation | MATHEMATICS, APPLIED | APPROXIMATION | INTEGRAL-EQUATIONS | ALGORITHMS | SCATTERING PROBLEMS | Lippmann-Schwinger equation | NUMERICAL-SOLUTION | acoustic scattering | penetrable media | adaptivity | HELMHOLTZ-EQUATION | integral equation | high-order accuracy | EFFICIENT | fast direct solver | electromagnetic scattering

Adaptivity | High-order accuracy | Electromagnetic scattering | Acoustic scattering | Penetrable media | Fast direct solver | Integral equation | Lippmann-schwinger equation | MATHEMATICS, APPLIED | APPROXIMATION | INTEGRAL-EQUATIONS | ALGORITHMS | SCATTERING PROBLEMS | Lippmann-Schwinger equation | NUMERICAL-SOLUTION | acoustic scattering | penetrable media | adaptivity | HELMHOLTZ-EQUATION | integral equation | high-order accuracy | EFFICIENT | fast direct solver | electromagnetic scattering

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2009, Volume 228, Issue 23, pp. 8872 - 8891

In this paper, we explore the Lax–Wendroff (LW) type time discretization as an alternative procedure to the high order Runge–Kutta time discretization adopted...

Conservative scheme | ALE method | Lax–Wendroff type time discretization | Lagrangian scheme | High order accuracy | ENO reconstruction | Lax-Wendroff type time discretization | EFFICIENT IMPLEMENTATION | ACCURATE | MESHES | ERRORS | PHYSICS, MATHEMATICAL | FLOW | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NONLINEAR HYPERBOLIC SYSTEMS | Reconstruction | Discretization | Partial differential equations | Runge-Kutta method | Computational efficiency | Derivatives | Euler equations | Two dimensional

Conservative scheme | ALE method | Lax–Wendroff type time discretization | Lagrangian scheme | High order accuracy | ENO reconstruction | Lax-Wendroff type time discretization | EFFICIENT IMPLEMENTATION | ACCURATE | MESHES | ERRORS | PHYSICS, MATHEMATICAL | FLOW | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NONLINEAR HYPERBOLIC SYSTEMS | Reconstruction | Discretization | Partial differential equations | Runge-Kutta method | Computational efficiency | Derivatives | Euler equations | Two dimensional

Journal Article

16.