Computational Geosciences, ISSN 1420-0597, 3/2012, Volume 16, Issue 2, pp. 297 - 322

Accurate geological modelling of features such as faults, fractures or erosion requires grids that are flexible with respect to geometry. Such grids generally...

Mimetic schemes | Unstructured grids | Hydrogeology | MPFA methods | Rate optimisation | Geotechnical Engineering & Applied Earth Sciences | Mathematics | Mathematical Modeling and Industrial Mathematics | Open-source implementation | Consistent discretisations | Soil Science & Conservation | Multiscale methods | MIXED FINITE-ELEMENTS | SIMULATION | FLOW | ELLIPTIC PROBLEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GEOSCIENCES, MULTIDISCIPLINARY | MULTISCALE METHOD | POROUS-MEDIA | Computer software industry | Analysis | Public software | Oil recovery | Open source software | Routines | Freeware | Computational fluid dynamics | Computation | Tools | Data structures | Mathematical models

Mimetic schemes | Unstructured grids | Hydrogeology | MPFA methods | Rate optimisation | Geotechnical Engineering & Applied Earth Sciences | Mathematics | Mathematical Modeling and Industrial Mathematics | Open-source implementation | Consistent discretisations | Soil Science & Conservation | Multiscale methods | MIXED FINITE-ELEMENTS | SIMULATION | FLOW | ELLIPTIC PROBLEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GEOSCIENCES, MULTIDISCIPLINARY | MULTISCALE METHOD | POROUS-MEDIA | Computer software industry | Analysis | Public software | Oil recovery | Open source software | Routines | Freeware | Computational fluid dynamics | Computation | Tools | Data structures | Mathematical models

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2014, Volume 36, Issue 3, pp. A955 - A983

This paper deals with the construction of a class of high-order accurate residual distribution schemes for advection-diffusion problems using conformal meshes....

Advection-diffusion problem | Unstructured meshes | Residual distribution schemes | Higher order schemes | MATHEMATICS, APPLIED | advection-diffusion problem | higher order schemes | residual distribution schemes | MULTIDIMENSIONAL UPWIND | unstructured meshes | Modeling and Simulation | Numerical Analysis | Computer Science | Mechanics | Mechanics of the fluids | Mathematics | Physics

Advection-diffusion problem | Unstructured meshes | Residual distribution schemes | Higher order schemes | MATHEMATICS, APPLIED | advection-diffusion problem | higher order schemes | residual distribution schemes | MULTIDIMENSIONAL UPWIND | unstructured meshes | Modeling and Simulation | Numerical Analysis | Computer Science | Mechanics | Mechanics of the fluids | Mathematics | Physics

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 02/2018, Volume 319, pp. 337 - 354

Two-dimensional simulations are carried out to assess standard grid adaptation criteria, widely used for ideal flows, for steady inviscid flows in the...

Van der Waals fluids | Finite volume scheme | Unstructured mesh adaptation | Under-expanded jets | Non-Ideal Compressible-fluid dynamics (NICFD) | CFD | MATHEMATICS, APPLIED | NOZZLES | COMPUTATIONS | SOLVERS | PREDICTION | DYNAMICS | JETS | ANISOTROPIC MESH ADAPTATION | SIMULATIONS | TECHNOLOGY | Thermodynamics | Anisotropy | Analysis | Fluid dynamics | Modeling and Simulation | Mathematics | Engineering Sciences | Numerical Analysis | Computer Science

Van der Waals fluids | Finite volume scheme | Unstructured mesh adaptation | Under-expanded jets | Non-Ideal Compressible-fluid dynamics (NICFD) | CFD | MATHEMATICS, APPLIED | NOZZLES | COMPUTATIONS | SOLVERS | PREDICTION | DYNAMICS | JETS | ANISOTROPIC MESH ADAPTATION | SIMULATIONS | TECHNOLOGY | Thermodynamics | Anisotropy | Analysis | Fluid dynamics | Modeling and Simulation | Mathematics | Engineering Sciences | Numerical Analysis | Computer Science

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 05/2017, Volume 84, Issue 3, pp. 135 - 151

Summary The simple low‐dissipation advection upwind splitting method (SLAU) scheme is a parameter‐free, low‐dissipation upwind scheme that has been applied in...

SLAU scheme | hybrid scheme | unstructured grids | scalar dissipation term | momentum fluxes | shock instabilities | INSTABILITY | CYLINDER | PHYSICS, FLUIDS & PLASMAS | APPROXIMATE RIEMANN SOLVERS | EQUATIONS | UPWIND METHODS | SIMULATION | WAVE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CURES | EULER | CARBUNCLE PHENOMENON | Shock | Numerical analysis | Fluctuations | Stability | Computer simulation | Momentum | Fluxes | Upwind schemes (mathematics) | Accuracy | Robustness (mathematics) | Dissipation | Unstructured grids (mathematics) | Detection | Weighting functions | Mach number | Mathematical analysis | Flux | Instability | Mathematical models

SLAU scheme | hybrid scheme | unstructured grids | scalar dissipation term | momentum fluxes | shock instabilities | INSTABILITY | CYLINDER | PHYSICS, FLUIDS & PLASMAS | APPROXIMATE RIEMANN SOLVERS | EQUATIONS | UPWIND METHODS | SIMULATION | WAVE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CURES | EULER | CARBUNCLE PHENOMENON | Shock | Numerical analysis | Fluctuations | Stability | Computer simulation | Momentum | Fluxes | Upwind schemes (mathematics) | Accuracy | Robustness (mathematics) | Dissipation | Unstructured grids (mathematics) | Detection | Weighting functions | Mach number | Mathematical analysis | Flux | Instability | Mathematical models

Journal Article

Numerische Mathematik, ISSN 0029-599X, 11/2006, Volume 105, Issue 1, pp. 35 - 71

We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an...

Numerical and Computational Methods | Finite volume scheme | Mathematical Methods in Physics | Unstructured grids | Mathematical and Computational Physics | Numerical Analysis | Appl.Mathematics/Computational Methods of Engineering | Mathematics, general | Mathematics | Irregular grids | Anisotropic heterogeneous diffusion problems | MATHEMATICS, APPLIED | DISCRETIZATION | unstructured grids | 2ND-ORDER ELLIPTIC PROBLEMS | ELEMENT METHODS | COEFFICIENTS | EQUATIONS | irregular grids | CONVERGENCE | MEDIA | anisotropic heterogeneous diffusion problems | finite volume scheme | Anisotropy

Numerical and Computational Methods | Finite volume scheme | Mathematical Methods in Physics | Unstructured grids | Mathematical and Computational Physics | Numerical Analysis | Appl.Mathematics/Computational Methods of Engineering | Mathematics, general | Mathematics | Irregular grids | Anisotropic heterogeneous diffusion problems | MATHEMATICS, APPLIED | DISCRETIZATION | unstructured grids | 2ND-ORDER ELLIPTIC PROBLEMS | ELEMENT METHODS | COEFFICIENTS | EQUATIONS | irregular grids | CONVERGENCE | MEDIA | anisotropic heterogeneous diffusion problems | finite volume scheme | Anisotropy

Journal Article

Computer Graphics Forum, ISSN 0167-7055, 05/2017, Volume 36, Issue 2, pp. 495 - 507

A key advantage of working with structured grids (e.g., images) is the ability to directly tap into the powerful machinery of linear algebra. This is not much...

I.3.1 [Computer Graphics]: Hardware Architecture—Graphics processors | G.1.0 [Mathematics of Computing]: General—Parallel algorithms | I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems | I.3.6 [Computer Graphics]: Methodology and Techniques — Graphics data structures and data types | G.1.3 [Mathematics of Computing]: Numerical Linear Algebra — Sparse, structured, and very large systems | Categories and Subject Descriptors (according to ACM CCS) | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MULTIPLICATION | Graphics software | Analysis | Algebra | Multiplication | Matrix algebra | Graphics processing units | Data structures | Vector processing (computers) | Matrix methods | Machinery | Computer memory | Finite element method | Computer peripherals | Sparsity | Matrix representation | Mathematical analysis | Linear algebra | Computer graphics | Structured grids (mathematics) | Hardware | Unstructured grids (mathematics)

I.3.1 [Computer Graphics]: Hardware Architecture—Graphics processors | G.1.0 [Mathematics of Computing]: General—Parallel algorithms | I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems | I.3.6 [Computer Graphics]: Methodology and Techniques — Graphics data structures and data types | G.1.3 [Mathematics of Computing]: Numerical Linear Algebra — Sparse, structured, and very large systems | Categories and Subject Descriptors (according to ACM CCS) | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MULTIPLICATION | Graphics software | Analysis | Algebra | Multiplication | Matrix algebra | Graphics processing units | Data structures | Vector processing (computers) | Matrix methods | Machinery | Computer memory | Finite element method | Computer peripherals | Sparsity | Matrix representation | Mathematical analysis | Linear algebra | Computer graphics | Structured grids (mathematics) | Hardware | Unstructured grids (mathematics)

Journal Article

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 07/2014, Volume 24, Issue 8, pp. 1575 - 1619

We present Finite Volume methods for diffusion equations on generic meshes, that received important coverage in the last decade or so. After introducing the...

Elliptic equation | Discrete duality finite volume schemes | Coercivity | Minimum and maximum principles | Multi-point flux approximation | Review | Monotony | Finite volume schemes | Hybrid mimetic mixed methods | Convergence analysis | DISCRETE DUALITY | MATHEMATICS, APPLIED | coercivity | hybrid mimetic mixed methods | multi-point flux approximation | monotony | GENERAL 2D MESHES | convergence analysis | MULTIPOINT FLUX APPROXIMATION | QUADRILATERAL GRIDS | TENSOR PRESSURE EQUATION | DIFFERENCE METHOD | discrete duality finite volume schemes | UNSTRUCTURED POLYHEDRAL MESHES | NONLINEAR ELLIPTIC-EQUATIONS | POLYGONAL MESHES | finite volume schemes | minimum and maximum principles | CENTERED GALERKIN METHODS | elliptic equation | Mathematics - Numerical Analysis

Elliptic equation | Discrete duality finite volume schemes | Coercivity | Minimum and maximum principles | Multi-point flux approximation | Review | Monotony | Finite volume schemes | Hybrid mimetic mixed methods | Convergence analysis | DISCRETE DUALITY | MATHEMATICS, APPLIED | coercivity | hybrid mimetic mixed methods | multi-point flux approximation | monotony | GENERAL 2D MESHES | convergence analysis | MULTIPOINT FLUX APPROXIMATION | QUADRILATERAL GRIDS | TENSOR PRESSURE EQUATION | DIFFERENCE METHOD | discrete duality finite volume schemes | UNSTRUCTURED POLYHEDRAL MESHES | NONLINEAR ELLIPTIC-EQUATIONS | POLYGONAL MESHES | finite volume schemes | minimum and maximum principles | CENTERED GALERKIN METHODS | elliptic equation | Mathematics - Numerical Analysis

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 11/2019, Volume 91, Issue 8, pp. 395 - 418

Summary A novel wetting and drying treatment for second‐order Runge‐Kutta discontinuous Galerkin methods solving the nonlinear shallow‐water equations is...

shallow‐water equations | wetting and drying | discontinuous Galerkin methods | well‐balanced schemes | stability | limiter | Nonlinear equations | Stability | Wetting | Preservation | Nondestructive testing | Benchmarks | Momentum | Integrators | Stability analysis | Parameter sensitivity | Equations | Inundation | Constraining | Robustness (mathematics) | Galerkin method | Unstructured grids (mathematics) | Drying | Mathematics - Numerical Analysis

shallow‐water equations | wetting and drying | discontinuous Galerkin methods | well‐balanced schemes | stability | limiter | Nonlinear equations | Stability | Wetting | Preservation | Nondestructive testing | Benchmarks | Momentum | Integrators | Stability analysis | Parameter sensitivity | Equations | Inundation | Constraining | Robustness (mathematics) | Galerkin method | Unstructured grids (mathematics) | Drying | Mathematics - Numerical Analysis

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 2/2016, Volume 66, Issue 2, pp. 692 - 724

In this paper we generalise to non-uniform grids of quad-tree type the Compact WENO reconstruction of Levy et al. (SIAM J Sci Comput 22(2):656–672, 2000), thus...

Computational Mathematics and Numerical Analysis | Algorithms | High order finite volumes | 65M08 | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | 65M50 | Numerical entropy production | 65M12 | h-adaptivity | MATHEMATICS, APPLIED | NONLINEAR CONSERVATION-LAWS | EFFICIENT IMPLEMENTATION | GENERIC GRID INTERFACE | GLOBAL ACCURACY | ESSENTIALLY NONOSCILLATORY SCHEMES | TIME | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | WAVE-PROPAGATION ALGORITHMS | PARALLEL | Reconstruction | Errors | Computation | Decay | Mathematical models | Runge-Kutta method | Neighbouring | Entropy | Mathematics - Numerical Analysis

Computational Mathematics and Numerical Analysis | Algorithms | High order finite volumes | 65M08 | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | 65M50 | Numerical entropy production | 65M12 | h-adaptivity | MATHEMATICS, APPLIED | NONLINEAR CONSERVATION-LAWS | EFFICIENT IMPLEMENTATION | GENERIC GRID INTERFACE | GLOBAL ACCURACY | ESSENTIALLY NONOSCILLATORY SCHEMES | TIME | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | WAVE-PROPAGATION ALGORITHMS | PARALLEL | Reconstruction | Errors | Computation | Decay | Mathematical models | Runge-Kutta method | Neighbouring | Entropy | Mathematics - Numerical Analysis

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 12/2019, Volume 357, p. 112584

In this article, we developed an unstructured fluid solver based on finite volume framework for the low-Mach number compressible flows. The present method,...

Low-Mach number | High-order reconstruction | Finite volume method | Navier–Stokes equation | Unstructured grid | Incompressible limit | WEIGHTED ENO SCHEMES | WENO SCHEMES | UNIFIED FORMULATION | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | Navier-Stokes equation | HIGH-ORDER ACCURATE | FINITE-VOLUME METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | ENGINEERING, MULTIDISCIPLINARY | LARGE-EDDY SIMULATION | INCOMPRESSIBLE FLOWS | Reconstruction | Computational fluid dynamics | Fluid flow | Smoothness | Forecasting | Constraining | Incompressible flow | Accuracy | Algorithms | Robustness (mathematics) | Energy dissipation | Numerical dissipation | Polynomials | Numerical models | Unstructured grids (mathematics) | Compressible flow | Mach number | Viscous flow | Mechanics | Engineering Sciences | Fluids mechanics

Low-Mach number | High-order reconstruction | Finite volume method | Navier–Stokes equation | Unstructured grid | Incompressible limit | WEIGHTED ENO SCHEMES | WENO SCHEMES | UNIFIED FORMULATION | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | Navier-Stokes equation | HIGH-ORDER ACCURATE | FINITE-VOLUME METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | ENGINEERING, MULTIDISCIPLINARY | LARGE-EDDY SIMULATION | INCOMPRESSIBLE FLOWS | Reconstruction | Computational fluid dynamics | Fluid flow | Smoothness | Forecasting | Constraining | Incompressible flow | Accuracy | Algorithms | Robustness (mathematics) | Energy dissipation | Numerical dissipation | Polynomials | Numerical models | Unstructured grids (mathematics) | Compressible flow | Mach number | Viscous flow | Mechanics | Engineering Sciences | Fluids mechanics

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 11/2016, Volume 69, Issue 2, pp. 905 - 920

The flux reconstruction (FR) approach offers an efficient route to high-order accuracy on unstructured grids. In this work we study the effect of solution...

Computational Mathematics and Numerical Analysis | Algorithms | Flux reconstruction | High-order methods | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | Discontinuous galerkin | MATHEMATICS, APPLIED | SYMMETRIC QUADRATURE-RULES

Computational Mathematics and Numerical Analysis | Algorithms | Flux reconstruction | High-order methods | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Mathematics | Discontinuous galerkin | MATHEMATICS, APPLIED | SYMMETRIC QUADRATURE-RULES

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 11/2019, Volume 91, Issue 8, pp. 367 - 394

Summary A robust, adaptive unstructured mesh refinement strategy for high‐order Runge‐Kutta discontinuous Galerkin method is proposed. The present work mainly...

subcell limiter | Runge‐Kutta discontinuous Galerkin method | WENO method | adaptive mesh refinement | Euler equations | HWENO method | Computer simulation | Oscillations | Adaptive control | Finite element method | Robustness (mathematics) | Energy dissipation | Numerical dissipation | Inviscid flow | Strategy | Galerkin method | Gradient flow | Grid refinement (mathematics) | Unstructured grids (mathematics) | Compressible flow

subcell limiter | Runge‐Kutta discontinuous Galerkin method | WENO method | adaptive mesh refinement | Euler equations | HWENO method | Computer simulation | Oscillations | Adaptive control | Finite element method | Robustness (mathematics) | Energy dissipation | Numerical dissipation | Inviscid flow | Strategy | Galerkin method | Gradient flow | Grid refinement (mathematics) | Unstructured grids (mathematics) | Compressible flow

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 8/2018, Volume 44, Issue 4, pp. 1063 - 1090

Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic Poisson...

Visualization | Finite elements | Computational Mathematics and Numerical Analysis | Mathematical and Computational Biology | Coarse-grid projection | Mathematics | 65Y20 | 35Q30 | Computational Science and Engineering | Unstructured grids | Semi-implicit time integration | Pressure-correction schemes | Mathematical Modeling and Industrial Mathematics | 65N55 | 65N30 | MATHEMATICS, APPLIED | APPROXIMATION | BACKWARD-FACING STEP | ALGORITHM | LAMINAR-FLOW | DISCRETIZATIONS | SCHEME | PRESSURE | NAVIER-STOKES EQUATIONS | CIRCULAR-CYLINDER | MULTIGRID METHOD

Visualization | Finite elements | Computational Mathematics and Numerical Analysis | Mathematical and Computational Biology | Coarse-grid projection | Mathematics | 65Y20 | 35Q30 | Computational Science and Engineering | Unstructured grids | Semi-implicit time integration | Pressure-correction schemes | Mathematical Modeling and Industrial Mathematics | 65N55 | 65N30 | MATHEMATICS, APPLIED | APPROXIMATION | BACKWARD-FACING STEP | ALGORITHM | LAMINAR-FLOW | DISCRETIZATIONS | SCHEME | PRESSURE | NAVIER-STOKES EQUATIONS | CIRCULAR-CYLINDER | MULTIGRID METHOD

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2017, Volume 350, p. 45

A Godunov's type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around complex geometries is...

Compressibility | Turbulent flow | Computational fluid dynamics | Computer simulation | Reynolds number | Approximations | Fluid flow | Finite volume method | Finite element method | Operators (mathematics) | Accuracy | Simulation | Robustness (mathematics) | Numerical dissipation | Error correction | Unstructured grids (mathematics) | Numerical stability

Compressibility | Turbulent flow | Computational fluid dynamics | Computer simulation | Reynolds number | Approximations | Fluid flow | Finite volume method | Finite element method | Operators (mathematics) | Accuracy | Simulation | Robustness (mathematics) | Numerical dissipation | Error correction | Unstructured grids (mathematics) | Numerical stability

Journal Article

Numerische Mathematik, ISSN 0029-599X, 11/2016, Volume 134, Issue 3, pp. 637 - 666

In this paper, we develop a multigrid method on unstructured shape-regular grids. For a general shape-regular unstructured grid of $${\mathcal O}(N)$$ O ( N )...

Finite elements | Theoretical, Mathematical and Computational Physics | Mathematics | Clustering | Mathematical Methods in Physics | Auxiliary space | 65F10 | Multigrid | Numerical Analysis | Appl.Mathematics/Computational Methods of Engineering | Mathematics, general | Numerical and Computational Physics, Simulation | 65N22 | 65N55 | 65N30 | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | SPACES | BOUNDARY | ALGORITHMS | SMOOTHED AGGREGATION

Finite elements | Theoretical, Mathematical and Computational Physics | Mathematics | Clustering | Mathematical Methods in Physics | Auxiliary space | 65F10 | Multigrid | Numerical Analysis | Appl.Mathematics/Computational Methods of Engineering | Mathematics, general | Numerical and Computational Physics, Simulation | 65N22 | 65N55 | 65N30 | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | SPACES | BOUNDARY | ALGORITHMS | SMOOTHED AGGREGATION

Journal Article

Computational and Applied Mathematics, ISSN 2238-3603, 12/2019, Volume 38, Issue 4, pp. 1 - 25

We address the problem of inverse design of linear hyperbolic transport equations in 2D heterogeneous media. We develop numerical algorithms based on...

Computational Mathematics and Numerical Analysis | Adjoint | 35L04 | Mathematics | Inverse design | Linear transport | Gradient descent method | Sensitivity | First and second order schemes | 93B00 | Mathematical Applications in Computer Science | Applications of Mathematics | 49M04 | Mathematical Applications in the Physical Sciences | SHAPE OPTIMIZATION | MATHEMATICS, APPLIED | DESCENT | PARTIAL-DIFFERENTIAL-EQUATIONS | LIMITERS | CONTROLLABILITY | SCHEMES

Computational Mathematics and Numerical Analysis | Adjoint | 35L04 | Mathematics | Inverse design | Linear transport | Gradient descent method | Sensitivity | First and second order schemes | 93B00 | Mathematical Applications in Computer Science | Applications of Mathematics | 49M04 | Mathematical Applications in the Physical Sciences | SHAPE OPTIMIZATION | MATHEMATICS, APPLIED | DESCENT | PARTIAL-DIFFERENTIAL-EQUATIONS | LIMITERS | CONTROLLABILITY | SCHEMES

Journal Article