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1. Full Text Review of summation-by-parts schemes for initial–boundary-value problems
by Svärd, Magnus and Nordström, Jan and Beräkningsmatematik and Linköpings universitet and Matematiska institutionen and Tekniska högskolan
Journal of Computational Physics, ISSN 0021-9991, 07/2014, Volume 268, pp. 17 - 38
High-order finite difference methods are efficient, easy to program, scale well in multiple dimensions and can be modified locally for various reasons (such as... 
Summation-by-Parts schemes | Simultaneous Approximation Terms | NONLINEAR CONSERVATION-LAWS | FINITE-DIFFERENCE SCHEMES | ORDER NUMERICAL-SIMULATION | ENTROPY-STABLE SCHEMES | SHARP SHOCK RESOLUTION | EFFICIENT SOLUTION STRATEGY | PHYSICS, MATHEMATICAL | CONJUGATE HEAT-TRANSFER | RUNGE-KUTTA SCHEMES | TIME-DEPENDENT PROBLEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | Operators | Construction | Stability | Computation | Mathematical analysis | Boundary conditions | Boundaries | Finite difference method | Mathematics - Numerical Analysis | Naturvetenskap | Computational Mathematics | Mathematics | Well posed problems; Energy estimates; Finite difference; Finite volume; Boundary conditions; Interface conditions; Stability; High order of accuracy | Natural Sciences | Beräkningsmatematik | Matematik
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2. Full Text Very-high-order weno schemes
by Gerolymos, G.A and Sénéchal, D and Vallet, I
Journal of Computational Physics, ISSN 0021-9991, 2009, Volume 228, Issue 23, pp. 8481 - 8524
We study (2 − 1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000)... 
Hyperbolic conservation laws | weno schemes | High-order schemes | Euler equations | Smoothness indicators | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | 2-DIMENSIONAL GAS-DYNAMICS | PHYSICS, MATHEMATICAL | WEIGHTED-ENO SCHEMES | RIEMANN PROBLEM | WENO schemes | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | TIME DISCRETIZATION METHODS | HYPERBOLIC CONSERVATION-LAWS | PRESERVING RUNGE-KUTTA | Environmental law | Algorithms | Conservation laws | Reconstruction | Exponents | Nonlinearity | Scalars | Adjustable | Optimization
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3. Full Text A parameter‐free ε‐adaptive algorithm for improving weighted compact nonlinear schemes
by Zheng, Shichao and Deng, Xiaogang and Wang, Dongfang and Xie, Chunhui
International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 06/2019, Volume 90, Issue 5, pp. 247 - 266
Summary In this paper, we propose a parameter‐free algorithm to calculate ε, a parameter of small quantity initially introduced into the nonlinear weights of... 
adaptive algorithm | critical points | numerical oscillations | resolution | WENO/WCNS | EFFICIENT IMPLEMENTATION | WENO SCHEMES | PHYSICS, FLUIDS & PLASMAS | WENO | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | ACCURACY | DIRECT NUMERICAL-SIMULATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | IMPROVEMENT | WCNS | FLOWS | OSCILLATIONS | Flow structures | Adaptive structures | Parameters | Adaptive algorithms | Oscillations | Critical point | Smoothness | Interpolation | Algorithms | Energy dissipation | Numerical dissipation | New orders | Computer applications
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4. Full Text Optimized prefactored compact schemes
by Ashcroft, Graham and Zhang, Xin
Journal of Computational Physics, ISSN 0021-9991, 2003, Volume 190, Issue 2, pp. 459 - 477
The numerical simulation of aeroacoustic phenomena requires high-order accurate numerical schemes with low dispersion and dissipation errors. In this paper we... 
High-order finite-difference | Computational aeroacoustics | Optimized compact differencing | ACOUSTICS | computational acroacoustics | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FINITE-DIFFERENCE SCHEMES | BOUNDARY-CONDITIONS | RESOLUTION | COMPUTATIONAL AEROACOUSTICS | PHYSICS, MATHEMATICAL | optimized compact differencing | high-order finite-difference
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5. Full Text High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger/Gross–Pitaevskii equations
by Antoine, Xavier and Besse, Christophe and Rispoli, Vittorio
Journal of Computational Physics, ISSN 0021-9991, 12/2016, Volume 327, pp. 252 - 269
The aim of this paper is to build and validate some explicit high-order schemes, both in space and time, for simulating the dynamics of systems of nonlinear... 
Gross–Pitaevskii equation | Pseudo-spectral schemes | Adaptive time stepping | Dynamics | Bose–Einstein condensates | Time-splitting | Nonlinear Schrödinger equation | Spin-orbit | High-order discretization | IMplicit–EXplicit schemes | STATES | RUNGE-KUTTA METHODS | Nonlinear Schrodinger equation | Gross-Pitaevskii equation | IMplicit-EXplicit schemes | PHYSICS, MATHEMATICAL | SPLITTING METHODS | MATLAB TOOLBOX | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Bose-Einstein condensates | COMPUTATION | EFFICIENT | GPELAB | Numerical Analysis | Analysis of PDEs | Mathematics
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6. Full Text NURBS-enhanced maximum-entropy schemes
by Greco, F and Coox, L and Maurin, F and Desmet, W
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 04/2017, Volume 317, pp. 580 - 597
In this paper, we combine high order local maximum-entropy schemes (HOLMES) with the integration framework developed in the NURBS-enhanced finite element... 
NURBS-enhanced FEM | High order | Maximum-entropy | Meshless | 2ND-ORDER | ARBITRARY ORDER | ISOGEOMETRIC ANALYSIS | METHOD NEFEM | MESHFREE APPROXIMANTS | FEM | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | APPROXIMATION SCHEMES | FINITE-ELEMENT-METHOD | SEAMLESS BRIDGE | GEOMETRY | Mechanical engineering
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7. Full Text Arbitrary-Lagrangian–Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes
by Boscheri, Walter and Dumbser, Michael
Journal of Computational Physics, ISSN 0021-9991, 10/2017, Volume 346, pp. 449 - 479
We present a new family of high order accurate one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of... 
Hyperbolic and parabolic PDE | Arbitrary-Lagrangian–Eulerian (ALE) Discontinuous Galerkin (DG) schemes | Moving unstructured meshes with local rezoning | Inertial Confinement Fusion (ICF) flows | High order of accuracy in space and time | Euler, MHD and Navier–Stokes equations | TRIANGULAR MESHES | ELEMENT-METHOD | TETRAHEDRAL MESHES | HIGH-ORDER | PHYSICS, MATHEMATICAL | GODUNOV-TYPE SCHEMES | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | ADER SCHEMES | BALANCE LAWS | Arbitrary-Lagrangian-Eulerian (ALE) | Discontinuous Galerkin (DG) schemes | Euler, MHD and Navier-Stokes equations | HYPERBOLIC CONSERVATION-LAWS | Analysis | Laser-plasma interactions | Algorithms | Pellet fusion
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8. Full Text ADER-WENO finite volume schemes with space–time adaptive mesh refinement
by Dumbser, Michael and Zanotti, Olindo and Hidalgo, Arturo and Balsara, Dinshaw S
Journal of Computational Physics, ISSN 0021-9991, 09/2013, Volume 248, pp. 257 - 286
We present the first high order one-step ADER-WENO finite volume scheme with adaptive mesh refinement (AMR) in multiple space dimensions. High order spatial... 
Hyperbolic conservation laws | Adaptive mesh refinement (AMR) | Time accurate local timestepping | MHD equations | ADER approach | Space–time adaptive grids | High order WENO reconstruction | Euler equations | Local space–time DG predictor | Space-time adaptive grids | Local space-time DG predictor | GENERALIZED RIEMANN PROBLEM | TANG VORTEX SYSTEM | EFFICIENT IMPLEMENTATION | FLUID-DYNAMICS | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | HIGH-ORDER | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | Analysis | Algorithms
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9. Full Text An improved WENO-Z scheme
by Acker, F and B. de R. Borges, R and Costa, B
Journal of Computational Physics, ISSN 0021-9991, 05/2016, Volume 313, pp. 726 - 753
In this article, we show that for a WENO scheme to improve the numerical resolution of smooth waves, increasing to some extent the contribution of the... 
WENO schemes | Hyperbolic conservation laws | High resolution shock capturing schemes | Smoothness indicators | High-order methods | EFFICIENT IMPLEMENTATION | SMOOTHNESS INDICATOR | ESSENTIALLY NONOSCILLATORY SCHEMES | SIMULATION | PHYSICS, MATHEMATICAL | FLOW | ACCURACY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HYPERBOLIC CONSERVATION-LAWS | Discontinuity | Accuracy | Computation | Dissipation | Mathematical models | Critical point | Smoothness | Numerical stability
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10. Full Text A new class of central compact schemes with spectral-like resolution II: Hybrid weighted nonlinear schemes
by Liu, Xuliang and Zhang, Shuhai and Zhang, Hanxin and Shu, Chi-Wang
Journal of Computational Physics, ISSN 0021-9991, 03/2015, Volume 284, pp. 133 - 154
In this paper, we develop a class of nonlinear compact schemes based on our previous linear central compact schemes with spectral-like resolution (X. Liu et... 
High resolution | Low dissipation | Compact scheme | Weighted interpolation | WENO scheme | EFFICIENT IMPLEMENTATION | TURBULENCE INTERACTION | FINITE-DIFFERENCE SCHEMES | WENO SCHEMES | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | PHYSICS, MATHEMATICAL | ENO SCHEMES | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HYPERBOLIC CONSERVATION-LAWS | NUMERICAL-SIMULATION | Aerodynamics | Analysis | Discontinuity | Interpolation | Computer simulation | Dissipation | Flux | Nonlinearity | Spectra | Derivatives | Fluxes
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11. Full Text Optimal Runge–Kutta schemes for pseudo time-stepping with high-order unstructured methods
by Vermeire, B.C and Loppi, N.A and Vincent, P.E
Journal of Computational Physics, ISSN 0021-9991, 04/2019, Volume 383, pp. 55 - 71
In this study we generate optimal Runge–Kutta (RK) schemes for converging the Artificial Compressibility Method (ACM) using dual time-stepping with high-order... 
Runge–Kutta | Flux reconstruction | Artificial compressibility | High-order | Optimal | Pseudo time-stepping | NUMBER | GRIDS | FLUX | PHYSICS, MATHEMATICAL | IMPLICIT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Runge-Kutta | TURBULENCE | CONSERVATION-LAWS | SIMULATIONS | FINITE-ELEMENT-METHOD | Turbulence | Bisphenol-A | Analysis | Methods | Aerospace engineering
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12. Full Text A new class of central compact schemes with spectral-like resolution I: Linear schemes
by Liu, Xuliang and Zhang, Shuhai and Zhang, Hanxin and Shu, Chi-Wang
Journal of Computational Physics, ISSN 0021-9991, 09/2013, Volume 248, pp. 235 - 256
In this paper, we design a new class of central compact schemes based on the cell-centered compact schemes of Lele [S.K. Lele, Compact finite difference... 
High resolution | Compact scheme | Computational aeroacoustics | Direct numerical simulation | EFFICIENT IMPLEMENTATION | COMPRESSIBLE TURBULENCE | FINITE-DIFFERENCE SCHEMES | HIGH-ORDER | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | DIRECT NUMERICAL-SIMULATION | DISSIPATIVE EXPLICIT SCHEMES | RUNGE-KUTTA SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SOUND | Turbulent flow | Computer simulation | Computation | Mathematical analysis | Dissipation | Mathematical models | Derivatives | Finite difference method
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13. Full Text Space–time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting
by Zanotti, Olindo and Fambri, Francesco and Dumbser, Michael and Hidalgo, Arturo
Computers and Fluids, ISSN 0045-7930, 09/2015, Volume 118, pp. 204 - 224
In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG) finite element method on space–time adaptive Cartesian meshes (AMR)... 
High order space–time adaptive mesh refinement (AMR) | Hyperbolic conservation laws | MOOD paradigm | ADER-DG and ADER-WENO finite volume schemes | A posteriori sub-cell finite volume limiter | Arbitrary high-order discontinuous Galerkin schemes | High order space-time adaptive mesh refinement (AMR) | HERMITE WENO SCHEMES | GENERALIZED RIEMANN PROBLEM | TANG VORTEX SYSTEM | EFFICIENT IMPLEMENTATION | ASYMPTOTIC-EXPANSION | HIGH-ORDER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MESH REFINEMENT | COMPRESSIBLE FLOW | CONSERVATION-LAWS | UNSTRUCTURED MESHES | Fluid dynamics | Environmental law | Magnetohydrodynamics | Fluids | Computational fluid dynamics | Mathematical analysis | Fluid flow | Mathematical models | Polynomials | Galerkin methods
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