Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 09/2017, Volume 324, pp. 170 - 203

In this paper a new high order semi-implicit discontinuous Galerkin method (SI-DG) is presented for the solution of the incompressible Navier–Stokes equations...

Space-time adaptive mesh refinement (AMR) | Staggered discontinuous Galerkin schemes | Incompressible Navier–Stokes equations | Staggered adaptive Cartesian grids | Spectral semi implicit DG schemes | CONVECTION-DIFFUSION PROBLEMS | COMPRESSIBLE FLOWS | BACKWARD-FACING STEP | SHALLOW-WATER EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PIECEWISE-LINEAR SYSTEMS | ENGINEERING, MULTIDISCIPLINARY | Incompressible Navier-Stokes equations | PARTIAL-DIFFERENTIAL-EQUATIONS | MESH REFINEMENT | CONSERVATION-LAWS | UNSTRUCTURED MESHES | FINITE-ELEMENT-METHOD | Mathematics - Numerical Analysis

Space-time adaptive mesh refinement (AMR) | Staggered discontinuous Galerkin schemes | Incompressible Navier–Stokes equations | Staggered adaptive Cartesian grids | Spectral semi implicit DG schemes | CONVECTION-DIFFUSION PROBLEMS | COMPRESSIBLE FLOWS | BACKWARD-FACING STEP | SHALLOW-WATER EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PIECEWISE-LINEAR SYSTEMS | ENGINEERING, MULTIDISCIPLINARY | Incompressible Navier-Stokes equations | PARTIAL-DIFFERENTIAL-EQUATIONS | MESH REFINEMENT | CONSERVATION-LAWS | UNSTRUCTURED MESHES | FINITE-ELEMENT-METHOD | Mathematics - Numerical Analysis

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2019, Volume 386, pp. 158 - 189

In most classical approaches of computational geophysics for seismic wave propagation problems, complex surface topography is either accounted for by...

Diffuse interface method (DIM) | High order schemes | Linear elasticity equations for seismic wave propagation | Adaptive mesh refinement (AMR) | Complex geometries | Discontinuous Galerkin schemes | 1ST-ORDER HYPERBOLIC FORMULATION | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | FREE-SURFACE | FINITE-VOLUME METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | TO-DETONATION TRANSITION | ORDER ADER SCHEMES | SPECTRAL ELEMENT METHOD | CONSERVATION-LAWS | STAGGERED UNSTRUCTURED MESHES | Wave propagation | Seismic waves | Seismology | Analysis | High resolution | Compressibility | Propagation | Elasticity | Mapping | Elastic waves | Characteristic functions | Complexity | Finite element method | Energy dissipation | Topography | Eigenvalues | Mathematical models | Mesh generation | Free surfaces | Discontinuity | Wave equations | Coordinates | Geophysics | Boundary conditions | Thickness | Problems | Unity | Computation | Galerkin method

Diffuse interface method (DIM) | High order schemes | Linear elasticity equations for seismic wave propagation | Adaptive mesh refinement (AMR) | Complex geometries | Discontinuous Galerkin schemes | 1ST-ORDER HYPERBOLIC FORMULATION | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | FREE-SURFACE | FINITE-VOLUME METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | TO-DETONATION TRANSITION | ORDER ADER SCHEMES | SPECTRAL ELEMENT METHOD | CONSERVATION-LAWS | STAGGERED UNSTRUCTURED MESHES | Wave propagation | Seismic waves | Seismology | Analysis | High resolution | Compressibility | Propagation | Elasticity | Mapping | Elastic waves | Characteristic functions | Complexity | Finite element method | Energy dissipation | Topography | Eigenvalues | Mathematical models | Mesh generation | Free surfaces | Discontinuity | Wave equations | Coordinates | Geophysics | Boundary conditions | Thickness | Problems | Unity | Computation | Galerkin method

Journal Article

Applied Numerical Mathematics, ISSN 0168-9274, 12/2016, Volume 110, pp. 41 - 74

In this paper two new families of arbitrary high order accurate spectral discontinuous Galerkin (DG) finite element methods are derived on staggered Cartesian...

Spectral space–time DG schemes | Spectral semi-implicit DG schemes | Staggered discontinuous Galerkin schemes | Incompressible Navier–Stokes equations | Staggered Cartesian grids | Arbitrary high order in space and time | Spectral space-time DG schemes | CONVECTION-DIFFUSION PROBLEMS | MATHEMATICS, APPLIED | COMPRESSIBLE FLOWS | BACKWARD-FACING STEP | ADAPTIVE MESH REFINEMENT | SHALLOW-WATER EQUATIONS | FREE-SURFACE FLOWS | PIECEWISE-LINEAR SYSTEMS | Incompressible Navier-Stokes equations | CONSERVATION-LAWS | UNSTRUCTURED MESHES | FINITE-ELEMENT-METHOD | Fluid dynamics | Methods | Mathematics - Numerical Analysis

Spectral space–time DG schemes | Spectral semi-implicit DG schemes | Staggered discontinuous Galerkin schemes | Incompressible Navier–Stokes equations | Staggered Cartesian grids | Arbitrary high order in space and time | Spectral space-time DG schemes | CONVECTION-DIFFUSION PROBLEMS | MATHEMATICS, APPLIED | COMPRESSIBLE FLOWS | BACKWARD-FACING STEP | ADAPTIVE MESH REFINEMENT | SHALLOW-WATER EQUATIONS | FREE-SURFACE FLOWS | PIECEWISE-LINEAR SYSTEMS | Incompressible Navier-Stokes equations | CONSERVATION-LAWS | UNSTRUCTURED MESHES | FINITE-ELEMENT-METHOD | Fluid dynamics | Methods | Mathematics - Numerical Analysis

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2007, Volume 224, Issue 1, pp. 150 - 167

Multiphase flows associated with interfacial dynamics, steep jumps in fluid properties and moving boundaries between different phases pose substantial...

Staggered grid | Immersed boundary | Adaptive Cartesian grid | Interface tracking | GEOMETRIES | adaptive Cartesian grid | SHARP-INTERFACE | interface tracking | staggered grid | COMPUTATIONS | PHYSICS, MATHEMATICAL | BUBBLES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | immersed boundary | CONNECTIVITY | DYNAMICS | LEVEL SET METHODS | FLUID METHOD | FRONT-TRACKING METHOD | MULTIPHASE FLOW | Analysis | Methods | Algorithms

Staggered grid | Immersed boundary | Adaptive Cartesian grid | Interface tracking | GEOMETRIES | adaptive Cartesian grid | SHARP-INTERFACE | interface tracking | staggered grid | COMPUTATIONS | PHYSICS, MATHEMATICAL | BUBBLES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | immersed boundary | CONNECTIVITY | DYNAMICS | LEVEL SET METHODS | FLUID METHOD | FRONT-TRACKING METHOD | MULTIPHASE FLOW | Analysis | Methods | Algorithms

Journal Article

Applied Ocean Research, ISSN 0141-1187, 10/2013, Volume 43, pp. 234 - 243

A new adaptive Cartesian-grid for the CIP (constrained interpolation profile) method is proposed and applied to two-dimensional numerical simulations of...

Staggered grid | Dam break | CIP | CCUP | Adaptive grid | Wave breaking | ENGINEERING, OCEAN | OCEANOGRAPHY | SIMULATION | Models | Algorithms | Analysis | Methods

Staggered grid | Dam break | CIP | CCUP | Adaptive grid | Wave breaking | ENGINEERING, OCEAN | OCEANOGRAPHY | SIMULATION | Models | Algorithms | Analysis | Methods

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 08/2019, Volume 390, pp. 548 - 594

This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined staggered...

Projection method preconditioner | Monolithic Navier-Stokes solver | Staggered Cartesian grid | Adaptive mesh refinement | Convective flux limiters | Level set method | ACCURATE | VOLUME | MODEL | PHYSICS, MATHEMATICAL | PROJECTION METHODS | CONSISTENT MASS | LEVEL-SET METHOD | IMPACT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FLUID | 2-PHASE FLOWS | DROPLET | Fluid dynamics | Specific gravity | Gravity | Formulations | Gravitation | Computational fluid dynamics | Computer simulation | Biological evolution | Fluid flow | Variations | Boundary conditions | Momentum | Convection | Flow stability | Mass balance | Incompressible flow | Accuracy | Density ratio | Algorithms | Robustness (mathematics) | Mathematical analysis | Multiphase | Vorticity | Surface tension | Transport | Navier-Stokes equations

Projection method preconditioner | Monolithic Navier-Stokes solver | Staggered Cartesian grid | Adaptive mesh refinement | Convective flux limiters | Level set method | ACCURATE | VOLUME | MODEL | PHYSICS, MATHEMATICAL | PROJECTION METHODS | CONSISTENT MASS | LEVEL-SET METHOD | IMPACT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FLUID | 2-PHASE FLOWS | DROPLET | Fluid dynamics | Specific gravity | Gravity | Formulations | Gravitation | Computational fluid dynamics | Computer simulation | Biological evolution | Fluid flow | Variations | Boundary conditions | Momentum | Convection | Flow stability | Mass balance | Incompressible flow | Accuracy | Density ratio | Algorithms | Robustness (mathematics) | Mathematical analysis | Multiphase | Vorticity | Surface tension | Transport | Navier-Stokes equations

Journal Article

Applied Numerical Mathematics, ISSN 0168-9274, 2006, Volume 56, Issue 6, pp. 778 - 799

Central schemes are frequently used for incompressible and compressible flow calculations. The present paper is the first in a forthcoming series where a new...

Hyperbolic conservation laws | 3D staggered grids | Finite volumes | Adaptive Cartesian meshes | Central schemes | MATHEMATICS, APPLIED | hyperbolic conservation laws | GRIDS | adaptive Cartesian meshes | finite volumes | central schemes | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME METHODS | Algorithms

Hyperbolic conservation laws | 3D staggered grids | Finite volumes | Adaptive Cartesian meshes | Central schemes | MATHEMATICS, APPLIED | hyperbolic conservation laws | GRIDS | adaptive Cartesian meshes | finite volumes | central schemes | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME METHODS | Algorithms

Journal Article

Sadhana, ISSN 0256-2499, 10/2014, Volume 39, Issue 5, pp. 1071 - 1094

A discrete forcing based Cartesian grid method is presented. The non-staggered arrangement of velocity and pressure is considered. The pressure gradient in...

Engineering | implicit | Engineering, general | viscous flow | Immersed boundary | non-staggered | CYLINDER | NUMERICAL-METHOD | FLUID-STRUCTURE INTERACTION | SIMULATION | FINITE-VOLUME METHOD | NAVIER-STOKES EQUATIONS | ENGINEERING, MULTIDISCIPLINARY | COMPUTATION | IMMERSED BOUNDARY METHOD | Reconstruction | Cartesian | Mathematical analysis | Dirichlet problem | Mathematical models | Boundaries | Grid method | Cylinders

Engineering | implicit | Engineering, general | viscous flow | Immersed boundary | non-staggered | CYLINDER | NUMERICAL-METHOD | FLUID-STRUCTURE INTERACTION | SIMULATION | FINITE-VOLUME METHOD | NAVIER-STOKES EQUATIONS | ENGINEERING, MULTIDISCIPLINARY | COMPUTATION | IMMERSED BOUNDARY METHOD | Reconstruction | Cartesian | Mathematical analysis | Dirichlet problem | Mathematical models | Boundaries | Grid method | Cylinders

Journal Article

Computers and Fluids, ISSN 0045-7930, 09/2013, Volume 84, pp. 231 - 246

•We develop an octree based finite difference method for incompressible viscous flows.•The method is shown to be stable, second order accurate and...

Octree grid | Staggered grid | MAC scheme | Benchmarking | Incompressible viscous fluid | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | FLUID | ADAPTIVE SOLVER | FLOW | Fluid dynamics | Public contracts | Analysis | Computational fluid dynamics | Mathematical analysis | Dissipation | Fluid flow | Mathematical models | Three dimensional | Cylinders | Navier-Stokes equations

Octree grid | Staggered grid | MAC scheme | Benchmarking | Incompressible viscous fluid | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | FLUID | ADAPTIVE SOLVER | FLOW | Fluid dynamics | Public contracts | Analysis | Computational fluid dynamics | Mathematical analysis | Dissipation | Fluid flow | Mathematical models | Three dimensional | Cylinders | Navier-Stokes equations

Journal Article

Numerical Linear Algebra with Applications, ISSN 1070-5325, 10/2018, Volume 25, Issue 5, pp. e2151 - n/a

Summary The goal of this paper is to create a fruitful bridge between the numerical methods for approximating PDEs in fluid dynamics and the (iterative)...

spectral symbol | Toeplitz matrices (block | multilevel | generating function | matrix sequence | spectral analysis | high‐order staggered finite element schemes | GLT analysis | staggered semi‐implicit discontinuous Galerkin schemes | incompressible Navier–Stokes equations | high-order staggered finite element schemes | staggered semi-implicit discontinuous Galerkin schemes | incompressible Navier-Stokes equations | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | CARTESIAN GRIDS | FINITE-ELEMENT APPROXIMATION | LOCALLY TOEPLITZ SEQUENCES | SHALLOW-WATER EQUATIONS | FREE-SURFACE FLOWS | MATHEMATICS | CONSERVATION-LAWS | SPATIAL DISCRETIZATION | Toeplitz matrices (block, multilevel) | MULTI-ITERATIVE TECHNIQUES | CONJUGATE GRADIENTS | Fluid dynamics | Analysis | Methods | Linear systems | Conjugate gradient method | Approximation | Computational fluid dynamics | Numerical methods | Fluid flow | Spectra | Convergence | Incompressible flow | Numerical analysis | Mathematical analysis | Solvers | Galerkin method | Iterative methods | Preconditioning | Navier-Stokes equations | Mathematics | Naturvetenskap | Natural Sciences | Beräkningsmatematik | Computational Mathematics | Matematik

spectral symbol | Toeplitz matrices (block | multilevel | generating function | matrix sequence | spectral analysis | high‐order staggered finite element schemes | GLT analysis | staggered semi‐implicit discontinuous Galerkin schemes | incompressible Navier–Stokes equations | high-order staggered finite element schemes | staggered semi-implicit discontinuous Galerkin schemes | incompressible Navier-Stokes equations | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | CARTESIAN GRIDS | FINITE-ELEMENT APPROXIMATION | LOCALLY TOEPLITZ SEQUENCES | SHALLOW-WATER EQUATIONS | FREE-SURFACE FLOWS | MATHEMATICS | CONSERVATION-LAWS | SPATIAL DISCRETIZATION | Toeplitz matrices (block, multilevel) | MULTI-ITERATIVE TECHNIQUES | CONJUGATE GRADIENTS | Fluid dynamics | Analysis | Methods | Linear systems | Conjugate gradient method | Approximation | Computational fluid dynamics | Numerical methods | Fluid flow | Spectra | Convergence | Incompressible flow | Numerical analysis | Mathematical analysis | Solvers | Galerkin method | Iterative methods | Preconditioning | Navier-Stokes equations | Mathematics | Naturvetenskap | Natural Sciences | Beräkningsmatematik | Computational Mathematics | Matematik

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2009, Volume 31, Issue 5, pp. 3979 - 3999

We present an explicit second-order finite volume generalization of the one-dimensional (1D) Nessyahu-Tadmor schemes for hyperbolic equations on adaptive...

3D adaptive central schemes | Unstructured staggered grid mesh adaptation | Finite volume methods | MATHEMATICS, APPLIED | TETRAHEDRAL GRIDS | EQUATIONS | MESH | finite volume methods | FINITE-VOLUME EXTENSION | CONVERGENCE | TRIANGULATIONS | LAX-FRIEDRICHS SCHEME | FLOWS | unstructured staggered grid mesh adaptation | HYPERBOLIC CONSERVATION-LAWS | Viscosity | Computational fluid dynamics | Mathematical analysis | Shock tubes | Software | Dynamical systems | Computer programs | Three dimensional

3D adaptive central schemes | Unstructured staggered grid mesh adaptation | Finite volume methods | MATHEMATICS, APPLIED | TETRAHEDRAL GRIDS | EQUATIONS | MESH | finite volume methods | FINITE-VOLUME EXTENSION | CONVERGENCE | TRIANGULATIONS | LAX-FRIEDRICHS SCHEME | FLOWS | unstructured staggered grid mesh adaptation | HYPERBOLIC CONSERVATION-LAWS | Viscosity | Computational fluid dynamics | Mathematical analysis | Shock tubes | Software | Dynamical systems | Computer programs | Three dimensional

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 12/2018, Volume 77, Issue 3, pp. 1490 - 1518

Staggered grid techniques have been applied successfully to many problems. A distinctive advantage is that physical laws arising from the corresponding partial...

Adaptive refinement | Computational Mathematics and Numerical Analysis | Staggered discontinuous Galerkin method | Algorithms | a-posteriori error estimate | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics | Error indicator | Convection–diffusion | MATHEMATICS, APPLIED | INTERIOR PENALTY | APPROXIMATION | Convection-diffusion | FINITE-ELEMENT METHODS | MAXWELLS EQUATIONS | DISCRETIZATIONS | ELLIPTIC PROBLEMS | PARTIAL-DIFFERENTIAL-EQUATIONS | HDG METHOD | WAVE-PROPAGATION | DG METHOD | Methods | Differential equations

Adaptive refinement | Computational Mathematics and Numerical Analysis | Staggered discontinuous Galerkin method | Algorithms | a-posteriori error estimate | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics | Error indicator | Convection–diffusion | MATHEMATICS, APPLIED | INTERIOR PENALTY | APPROXIMATION | Convection-diffusion | FINITE-ELEMENT METHODS | MAXWELLS EQUATIONS | DISCRETIZATIONS | ELLIPTIC PROBLEMS | PARTIAL-DIFFERENTIAL-EQUATIONS | HDG METHOD | WAVE-PROPAGATION | DG METHOD | Methods | Differential equations

Journal Article