Journal of Computational Physics, ISSN 0021-9991, 11/2019, Volume 397, p. 108858

We construct a space-time conservation element and solution element (CESE) scheme for solving the compressible Euler equations on moving meshes (CESE-MM) which...

Moving mesh | Computational fluid dynamics | The compressible Euler equations | Hybrid unstructured mesh | Space-time conservation element and solution element method | DISCONTINUOUS GALERKIN SCHEMES | ALE METHOD | TIME CONSERVATION ELEMENT | RIEMANN-SOLVERS | FLUID-STRUCTURE INTERACTION | COMPUTATIONAL METHODS | PHYSICS, MATHEMATICAL | REMAP | NONCONSERVATIVE HYPERBOLIC SYSTEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES | FINITE-VOLUME SCHEMES | Conservation laws | Compressibility | Robustness (mathematics) | Spacetime | Fluxes | Euler-Lagrange equation | Continuity (mathematics) | Riemann solver

Moving mesh | Computational fluid dynamics | The compressible Euler equations | Hybrid unstructured mesh | Space-time conservation element and solution element method | DISCONTINUOUS GALERKIN SCHEMES | ALE METHOD | TIME CONSERVATION ELEMENT | RIEMANN-SOLVERS | FLUID-STRUCTURE INTERACTION | COMPUTATIONAL METHODS | PHYSICS, MATHEMATICAL | REMAP | NONCONSERVATIVE HYPERBOLIC SYSTEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES | FINITE-VOLUME SCHEMES | Conservation laws | Compressibility | Robustness (mathematics) | Spacetime | Fluxes | Euler-Lagrange equation | Continuity (mathematics) | Riemann solver

Journal Article

Journal of Fluid Mechanics, ISSN 0022-1120, 02/2017, Volume 813, p. R4

We numerically investigate the direct initiation of detonations driven by the propagation of a blast wave into a unconfined gaseous combustible mixture to...

reacting flows | detonations | shock waves | TIME CONSERVATION ELEMENT | SCHEME | MECHANICS | PHYSICS, FLUIDS & PLASMAS | ENERGY-SOURCE | Transverse waves | Detonation | Compressibility | Two dimensional models | Chemical reactions | Euler-Lagrange equation | Equations | Risks | Studies | Gases | Wave propagation | Energy | Simulation | Dynamics | Breaking down | Sustainability | Spacetime | Flammability | Mathematical models | Yield | Interactions | Dimensional stability

reacting flows | detonations | shock waves | TIME CONSERVATION ELEMENT | SCHEME | MECHANICS | PHYSICS, FLUIDS & PLASMAS | ENERGY-SOURCE | Transverse waves | Detonation | Compressibility | Two dimensional models | Chemical reactions | Euler-Lagrange equation | Equations | Risks | Studies | Gases | Wave propagation | Energy | Simulation | Dynamics | Breaking down | Sustainability | Spacetime | Flammability | Mathematical models | Yield | Interactions | Dimensional stability

Journal Article

Computer Physics Communications, ISSN 0010-4655, 11/2018, Volume 232, pp. 165 - 176

We construct positivity-preserving space–time conservation element and solution element (CE/SE) schemes for solving the compressible Euler and Navier–Stokes...

Unstructured mesh | Positivity-preserving | The compressible Navier–Stokes equations | Space–time conservation element and solution element scheme | The compressible Euler equations | The compressible Navier-Stokes equations | DISCONTINUOUS GALERKIN SCHEMES | RIEMANN SOLVERS | TIME CONSERVATION ELEMENT | ACCURATE | PHYSICS, MATHEMATICAL | LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Space-time conservation element and solution element scheme | HIGH-RESOLUTION | SYSTEMS | FLOWS | EFFICIENT | FINITE-VOLUME SCHEMES

Unstructured mesh | Positivity-preserving | The compressible Navier–Stokes equations | Space–time conservation element and solution element scheme | The compressible Euler equations | The compressible Navier-Stokes equations | DISCONTINUOUS GALERKIN SCHEMES | RIEMANN SOLVERS | TIME CONSERVATION ELEMENT | ACCURATE | PHYSICS, MATHEMATICAL | LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Space-time conservation element and solution element scheme | HIGH-RESOLUTION | SYSTEMS | FLOWS | EFFICIENT | FINITE-VOLUME SCHEMES

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2013, Volume 35, Issue 1, pp. A351 - A377

We present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial...

Godunov-type methods | Wave propagation | High-order methods | Hyperbolic PDEs | WENO | DEFINITION | MATHEMATICS, APPLIED | hyperbolic PDEs | wave propagation | STABILITY | ERROR | high-order methods | FINITE-VOLUME METHODS | SHOCK-WAVES | Reconstruction | Algorithms | Discretization | Laws | Mathematical models | Fluxes | Computer programs

Godunov-type methods | Wave propagation | High-order methods | Hyperbolic PDEs | WENO | DEFINITION | MATHEMATICS, APPLIED | hyperbolic PDEs | wave propagation | STABILITY | ERROR | high-order methods | FINITE-VOLUME METHODS | SHOCK-WAVES | Reconstruction | Algorithms | Discretization | Laws | Mathematical models | Fluxes | Computer programs

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2019, Volume 397, p. 108775

We present a novel technique for the imposition of non-linear entropy conservative and entropy stable solid wall boundary conditions for the compressible...

Compressible Navier–Stokes equations | Entropy conservation | Summation-by-parts operators | Entropy stability | Simultaneous-approximation-terms | Solid wall | STABILITY | DIFFERENCE-SCHEMES | WAKE | PHYSICS, MATHEMATICAL | FLOW | TRANSITION | LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CIRCULAR-CYLINDER | DYNAMICS | SYSTEMS | EULER | Compressible Navier-Stokes equations | Supersonic flow | Operators | Compressibility | Approximation | Computational fluid dynamics | Computer simulation | Fluid flow | Boundary conditions | Entropy | Imposition | Adiabatic flow | Three dimensional flow | Robustness (mathematics) | Method of lines | Galerkin method | Unstructured grids (mathematics) | Dimensional stability | Navier-Stokes equations | Finite difference method

Compressible Navier–Stokes equations | Entropy conservation | Summation-by-parts operators | Entropy stability | Simultaneous-approximation-terms | Solid wall | STABILITY | DIFFERENCE-SCHEMES | WAKE | PHYSICS, MATHEMATICAL | FLOW | TRANSITION | LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CIRCULAR-CYLINDER | DYNAMICS | SYSTEMS | EULER | Compressible Navier-Stokes equations | Supersonic flow | Operators | Compressibility | Approximation | Computational fluid dynamics | Computer simulation | Fluid flow | Boundary conditions | Entropy | Imposition | Adiabatic flow | Three dimensional flow | Robustness (mathematics) | Method of lines | Galerkin method | Unstructured grids (mathematics) | Dimensional stability | Navier-Stokes equations | Finite difference method

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2017, Volume 330, p. 668

A maximum-principle-satisfying space-time conservation element and solution element (CE/SE) scheme is constructed to solve a reduced five-equation model...

Fluid mechanics | Compressibility | Equations of state | Spacetime | Conservation | Mathematical models | Maximum strategies | Navier Stokes equations

Fluid mechanics | Compressibility | Equations of state | Spacetime | Conservation | Mathematical models | Maximum strategies | Navier Stokes equations

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2012, Volume 34, Issue 4, pp. C210 - C231

Development of scientific software involves tradeoffs between ease of use, generality, and performance. We describe the design of a general hyperbolic PDE...

Wave propagation | Hyperbolic PDEs | Scientific software | Clawpack | Python | scientific software | MATHEMATICS, APPLIED | hyperbolic PDEs | wave propagation | Partial differential equations | Computation | Packages | Solvers | FORTRAN | Software | Computer programs | Matlab

Wave propagation | Hyperbolic PDEs | Scientific software | Clawpack | Python | scientific software | MATHEMATICS, APPLIED | hyperbolic PDEs | wave propagation | Partial differential equations | Computation | Packages | Solvers | FORTRAN | Software | Computer programs | Matlab

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 07/2015, Volume 292, pp. 88 - 113

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional...

Compressible Navier–Stokes equations | SBP-SAT | High-order discontinuous methods | Entropy | Entropy stability | Solid wall boundary conditions | Compressible Navier-stokes equations | SQUARE CYLINDER | FORM | PHYSICS, MATHEMATICAL | FLOW | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISCONTINUOUS GALERKIN | LARGE-EDDY SIMULATION | SYSTEMS | CONSERVATION-LAWS | OPERATORS | EULER | Compressible Navier-Stokes equations | SCHEMES | Fluid dynamics | Reconstruction | Operators | Stability | Mathematical analysis | Boundary conditions | Three dimensional | Navier-Stokes equations | Physics - Fluid Dynamics

Compressible Navier–Stokes equations | SBP-SAT | High-order discontinuous methods | Entropy | Entropy stability | Solid wall boundary conditions | Compressible Navier-stokes equations | SQUARE CYLINDER | FORM | PHYSICS, MATHEMATICAL | FLOW | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DISCONTINUOUS GALERKIN | LARGE-EDDY SIMULATION | SYSTEMS | CONSERVATION-LAWS | OPERATORS | EULER | Compressible Navier-Stokes equations | SCHEMES | Fluid dynamics | Reconstruction | Operators | Stability | Mathematical analysis | Boundary conditions | Three dimensional | Navier-Stokes equations | Physics - Fluid Dynamics

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 02/2020, Volume 92, Issue 2, pp. 79 - 93

Summary Time integration of Fourier pseudospectral DNS is usually performed using the classical fourth‐order accurate Runge‐Kutta method or other second‐ or...

error estimation | spectral | time integration | turbulent flow | adaptivity | incompressible flow | DIRECT NUMERICAL-SIMULATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | STATISTICS | PHYSICS, FLUIDS & PLASMAS

error estimation | spectral | time integration | turbulent flow | adaptivity | incompressible flow | DIRECT NUMERICAL-SIMULATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | STATISTICS | PHYSICS, FLUIDS & PLASMAS

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2018, Volume 56, Issue 1, pp. 256 - 273

We present an entropy stable numerical scheme subject to no-slip wall boundary conditions. To enforce entropy stability only the no-penetration boundary...

Nonlinear stability | Finite difference | Navier–Stokes | Wall boundary conditions | MATHEMATICS, APPLIED | nonlinear stability | NAVIER-STOKES EQUATIONS | STABLE SCHEMES | Navier-Stokes | CONSERVATION-LAWS | finite difference | wall boundary conditions

Nonlinear stability | Finite difference | Navier–Stokes | Wall boundary conditions | MATHEMATICS, APPLIED | nonlinear stability | NAVIER-STOKES EQUATIONS | STABLE SCHEMES | Navier-Stokes | CONSERVATION-LAWS | finite difference | wall boundary conditions

Journal Article

2014, ISBN 9783319016009, Volume 95, 11

Reference

Journal of Scientific Computing, ISSN 0885-7474, 11/2018, Volume 77, Issue 2, pp. 689 - 725

This work presents an entropy stable discontinuous Galerkin (DG) spectral element approximation for systems of non-linear conservation laws with general...

Discontinuous Galerkin | Computational Mathematics and Numerical Analysis | h / p Non-conforming mesh | Algorithms | Theoretical, Mathematical and Computational Physics | Summation-by-parts | Entropy stability | Mathematical and Computational Engineering | Mathematics | Entropy conservation | Non-linear hyperbolic conservation laws | h / p Non-conforming mesh | MATHEMATICS, APPLIED | NONLINEAR CONSERVATION-LAWS | GRIDS | FORM | SHALLOW-WATER EQUATIONS | ORDER | NAVIER-STOKES EQUATIONS | FINITE-DIFFERENCE METHODS | h/p Non-conforming mesh | SYSTEMS | OPERATORS | SCHEMES | Environmental law | Analysis | Methods | Naturvetenskap | Non-Linear Hyperbolic Conservation Laws | Computational Mathematics | Entropy Stability | Natural Sciences | Beräkningsmatematik | Summation-by-Parts | Matematik | h/p Non-Conforming Mesh | Entropy Conservation

Discontinuous Galerkin | Computational Mathematics and Numerical Analysis | h / p Non-conforming mesh | Algorithms | Theoretical, Mathematical and Computational Physics | Summation-by-parts | Entropy stability | Mathematical and Computational Engineering | Mathematics | Entropy conservation | Non-linear hyperbolic conservation laws | h / p Non-conforming mesh | MATHEMATICS, APPLIED | NONLINEAR CONSERVATION-LAWS | GRIDS | FORM | SHALLOW-WATER EQUATIONS | ORDER | NAVIER-STOKES EQUATIONS | FINITE-DIFFERENCE METHODS | h/p Non-conforming mesh | SYSTEMS | OPERATORS | SCHEMES | Environmental law | Analysis | Methods | Naturvetenskap | Non-Linear Hyperbolic Conservation Laws | Computational Mathematics | Entropy Stability | Natural Sciences | Beräkningsmatematik | Summation-by-Parts | Matematik | h/p Non-Conforming Mesh | Entropy Conservation

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2017, Volume 330, pp. 668 - 692

A maximum-principle-satisfying space-time conservation element and solution element (CE/SE) scheme is constructed to solve a reduced five-equation model...

Compressible multifluids | Maximum-principle-satisfying scheme | Five-equation model | Space-time conservation element and solution element (CE/SE) method | Upwind scheme | PHYSICS, MATHEMATICAL | MULTICOMPONENT FLOW CALCULATIONS | LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MIXTURE TYPE ALGORITHM | INTERFACE INTERACTION | HIGH-RESOLUTION SCHEMES | CAPTURING SCHEMES | MULTIMATERIAL FLOWS | FLUID METHOD | MULTIPHASE FLOW | EULER EQUATIONS | Mechanical engineering | Environmental law

Compressible multifluids | Maximum-principle-satisfying scheme | Five-equation model | Space-time conservation element and solution element (CE/SE) method | Upwind scheme | PHYSICS, MATHEMATICAL | MULTICOMPONENT FLOW CALCULATIONS | LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MIXTURE TYPE ALGORITHM | INTERFACE INTERACTION | HIGH-RESOLUTION SCHEMES | CAPTURING SCHEMES | MULTIMATERIAL FLOWS | FLUID METHOD | MULTIPHASE FLOW | EULER EQUATIONS | Mechanical engineering | Environmental law

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2015, Volume 290, pp. 132 - 138

Non-linear entropy stability and a summation-by-parts (SBP) framework are used to derive entropy stable interior interface coupling for the semi-discretized...

Compressible Navier–Stokes equations | High order discontinuous methods | Discontinuous interface coupling | Entropy stability | Summation-by-parts (SBP) operators | Compressible Navier-Stokes equations | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FORM | SYSTEMS | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | EULER | SCHEMES | Fluid dynamics | Reconstruction | Operators | Compressibility | Mathematical analysis | Joining | Entropy | Galerkin methods | Three dimensional | Navier-Stokes equations

Compressible Navier–Stokes equations | High order discontinuous methods | Discontinuous interface coupling | Entropy stability | Summation-by-parts (SBP) operators | Compressible Navier-Stokes equations | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FORM | SYSTEMS | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | EULER | SCHEMES | Fluid dynamics | Reconstruction | Operators | Compressibility | Mathematical analysis | Joining | Entropy | Galerkin methods | Three dimensional | Navier-Stokes equations

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2014, Volume 52, Issue 5, pp. 2227 - 2249

In practical computation with Runge–Kutta methods, the stage equations are not satisfied exactly, due to roundoff errors, algebraic solver errors, and so...

Mathematical extrapolation | Error rates | Mathematical theorems | Approximation | Algebra | Ordinary differential equations | Truncation errors | Polynomials | Runge Kutta method | Signal amplification | Extrapolation | Runge-Kutta methods | Strong stability preservation | Internal stability | Roundoff error | roundoff error | ordinary differential equations | MATHEMATICS, APPLIED | extrapolation | STABILITY | internal stability | strong stability preservation | CONVERGENCE | ORDINARY DIFFERENTIAL-EQUATIONS | SCHEMES

Mathematical extrapolation | Error rates | Mathematical theorems | Approximation | Algebra | Ordinary differential equations | Truncation errors | Polynomials | Runge Kutta method | Signal amplification | Extrapolation | Runge-Kutta methods | Strong stability preservation | Internal stability | Roundoff error | roundoff error | ordinary differential equations | MATHEMATICS, APPLIED | extrapolation | STABILITY | internal stability | strong stability preservation | CONVERGENCE | ORDINARY DIFFERENTIAL-EQUATIONS | SCHEMES

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2016, Volume 38, Issue 5, pp. A3129 - A3162

Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for the compressible Euler and Navier-Stokes equations...

Staggered grid | SBP-SAT | High-order accurate discontinuous methods | Compressible Navier-Stokes | Entropy stability | Conservation | MATHEMATICS, APPLIED | NONLINEAR CONSERVATION-LAWS | FINITE-DIFFERENCE SCHEMES | BOUNDARY-CONDITIONS | GALERKIN METHOD | staggered grid | VORTEX | compressible Navier-Stokes | entropy stability | conservation | QUADRATURE | SYSTEMS | high-order accurate discontinuous methods

Staggered grid | SBP-SAT | High-order accurate discontinuous methods | Compressible Navier-Stokes | Entropy stability | Conservation | MATHEMATICS, APPLIED | NONLINEAR CONSERVATION-LAWS | FINITE-DIFFERENCE SCHEMES | BOUNDARY-CONDITIONS | GALERKIN METHOD | staggered grid | VORTEX | compressible Navier-Stokes | entropy stability | conservation | QUADRATURE | SYSTEMS | high-order accurate discontinuous methods

Journal Article

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2016, Volume 9697, pp. 449 - 466

Conference Proceeding

Journal of Computational Acoustics, ISSN 0218-396X, 09/2011, Volume 19, Issue 3, pp. 241 - 268

The main goal of this paper is to develop an efficient numerical algorithm to compute the radiated far field noise provided by an unsteady flow field from...

Ffowcs WilliamsHawkings approach | nonlinear lowerupper symmetric GaussSeidel | LES | High-order spectral difference | FINITE VOLUME METHOD | ELEMENT METHOD | RECTANGULAR CYLINDERS | nonlinear lower-upper symmetric Gauss-Seidel | DISCONTINUOUS GALERKIN METHOD | CHEBYSHEV MULTIDOMAIN METHOD | UNSTRUCTURED GRIDS II | RESIDUAL DISTRIBUTION SCHEMES | ACOUSTICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Ffowcs Williams-Hawkings approach | ONE-DIMENSIONAL SYSTEMS | LARGE-EDDY SIMULATIONS | CONSERVATION-LAWS | Turbulent flow | Computer simulation | Laminar flow | Noise | Mathematical analysis | Mathematical models | Two dimensional | Cylinders

Ffowcs WilliamsHawkings approach | nonlinear lowerupper symmetric GaussSeidel | LES | High-order spectral difference | FINITE VOLUME METHOD | ELEMENT METHOD | RECTANGULAR CYLINDERS | nonlinear lower-upper symmetric Gauss-Seidel | DISCONTINUOUS GALERKIN METHOD | CHEBYSHEV MULTIDOMAIN METHOD | UNSTRUCTURED GRIDS II | RESIDUAL DISTRIBUTION SCHEMES | ACOUSTICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Ffowcs Williams-Hawkings approach | ONE-DIMENSIONAL SYSTEMS | LARGE-EDDY SIMULATIONS | CONSERVATION-LAWS | Turbulent flow | Computer simulation | Laminar flow | Noise | Mathematical analysis | Mathematical models | Two dimensional | Cylinders

Journal Article

21st AIAA International Space Planes and Hypersonics Technologies Conference, Hypersonics 2017, 2017

Conference Proceeding

10/2018

IJNMF 2019 Time integration of Fourier pseudo-spectral DNS is usually performed using the classical fourth-order accurate Runge--Kutta method, or other methods...

Journal Article

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