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1. Full Text Open-source MATLAB implementation of consistent discretisations on complex grids
by Lie, Knut–Andreas and Lie, Knut–Andreas and Krogstad, Stein and Krogstad, Stein and Ligaarden, Ingeborg Skjelkvåle and Ligaarden, Ingeborg Skjelkvåle and Natvig, Jostein Roald and Natvig, Jostein Roald and Nilsen, Halvor Møll and Nilsen, Halvor Møll and Skaflestad, Bård and Skaflestad, Bård
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
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2. Full Text High-order preserving residual distribution schemes for advection-diffusion scalar problems on arbitrary grids
by Abgrall, R and De Santis, D and Ricchiuto, M
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
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3. Full Text Assessment of grid adaptation criteria for steady, two-dimensional, inviscid flows in non-ideal compressible fluids
by Re, B and Dobrzynski, C and Guardone, A
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
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4. Full Text A robust low‐dissipation AUSM‐family scheme for numerical shock stability on unstructured grids
by Zhang, Fan and Liu, Jun and Chen, Biaosong and Zhong, Wanxie
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
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5. Full Text A mixed finite volume scheme for anisotropic diffusion problems on any grid
by Droniou, Jérôme and Eymard, Robert
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
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6. Full Text A GPU‐Adapted Structure for Unstructured Grids
by Zayer, Rhaleb and Steinberger, Markus and Seidel, Hans‐Peter
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)
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7. Full Text Finite volume schemes for diffusion equations: Introduction to and review of modern methods
by Droniou, Jerome
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
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8. Full Text A limiter‐based well‐balanced discontinuous Galerkin method for shallow‐water flows with wetting and drying: Triangular grids
by Vater, Stefan and Beisiegel, Nicole and Behrens, Jörn
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
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9. Full Text Adaptive Mesh Refinement for Hyperbolic Systems Based on Third-Order Compact WENO Reconstruction
by Semplice, M and Semplice, M and Coco, A and Coco, A and Russo, G and Russo, G
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
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10. Full Text High-fidelity solver on polyhedral unstructured grids for low-Mach number compressible viscous flow
by Xie, Bin and Deng, Xi and Liao, Shijun
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
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11. Full Text An Analysis of Solution Point Coordinates for Flux Reconstruction Schemes on Tetrahedral Elements
by Witherden, F D and Park, J S and Vincent, P E
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
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12. Full Text A high‐order Runge‐Kutta discontinuous Galerkin method with a subcell limiter on adaptive unstructured grids for two‐dimensional compressible inviscid flows
by Giri, Pritam and Qiu, Jianxian
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
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13. Full Text A finite-element coarse-grid projection method for incompressible flow simulations
by Kashefi, Ali and Kashefi, Ali and Staples, Anne E and Staples, Anne E
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
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14. Multiple-correction hybrid k-exact schemes for high-order compressible RANS-LES simulations on fully unstructured grids
by Grégoire Pont and Pierre Brenner and Paola Cinnella and Bruno Maugars and Jean-Christophe Robinet
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
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15. Full Text A nearly optimal multigrid method for general unstructured grids
by Grasedyck, Lars and Grasedyck, Lars and Wang, Lu and Wang, Lu and Xu, Jinchao and Xu, Jinchao
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
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16. Full Text Adjoint computational methods for 2D inverse design of linear transport equations on unstructured grids
by Morales-Hernández, M and Zuazua, E
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
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