High order modal Discontinuous Galerkin Implicit-Explicit Runge Kutta and Linear Multistep schemes for the Boltzmann model on general polygonal meshes

Computers & Fluids ◽

10.1016/j.compfluid.2021.105224 ◽

2021 ◽

pp. 105224

Author(s):

Walter Boscheri ◽

Giacomo Dimarco

Keyword(s):

Discontinuous Galerkin ◽

Polygonal Meshes ◽

Runge Kutta ◽

Boltzmann Model

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Numerical solution of 2D Euler equations for the transonic flow past over NACA0012 and RAE2822 airfoils using high order accurate Runge-Kutta Discontinuous Galerkin method

Proceedings of 2014 11th International Bhurban Conference on Applied Sciences & Technology (IBCAST) Islamabad, Pakistan, 14th - 18th January, 2014 ◽

10.1109/ibcast.2014.6778148 ◽

2014 ◽

Author(s):

Faheem Ahmed ◽

Fareed Ahmed ◽

Muhammad Affan ◽

Javed R Larik

Keyword(s):

Galerkin Method ◽

Numerical Solution ◽

Euler Equations ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Transonic Flow ◽

Flow Past ◽

2D Euler Equations ◽

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High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters on triangular meshes

Applied Numerical Mathematics ◽

10.1016/j.apnum.2020.03.013 ◽

2020 ◽

Vol 153 ◽

pp. 519-539

Author(s):

Jun Zhu ◽

Chi-Wang Shu ◽

Jianxian Qiu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Triangular Meshes ◽

New Type ◽

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Dispersion and Dissipation Error in High-Order Runge-Kutta Discontinuous Galerkin Discretisations of the Maxwell Equations

Journal of Scientific Computing ◽

10.1007/s10915-007-9143-y ◽

2007 ◽

Vol 33 (1) ◽

pp. 47-74 ◽

Author(s):

D. Sármány ◽

M. A. Botchev ◽

J. J. W. van der Vegt

Keyword(s):

Discontinuous Galerkin ◽

Maxwell Equations ◽

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A high‐order Runge‐Kutta discontinuous Galerkin method with a subcell limiter on adaptive unstructured grids for two‐dimensional compressible inviscid flows

International Journal for Numerical Methods in Fluids ◽

10.1002/fld.4757 ◽

2019 ◽

Vol 91 (8) ◽

pp. 367-394

Author(s):

Pritam Giri ◽

Jianxian Qiu

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Unstructured Grids ◽

Two Dimensional ◽

Inviscid Flows ◽

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A Runge-Kutta discontinuous Galerkin solver for 2D Boltzmann model equations: Verification and analysis of computational performance

10.1063/1.4769547 ◽

2012 ◽

Author(s):

Wei Su ◽

Alina A. Alexeenko ◽

Guobiao Cai

Keyword(s):

Discontinuous Galerkin ◽

Computational Performance ◽

Runge Kutta ◽

Model Equations ◽

Boltzmann Model

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A Problem-Independent Limiter for High-Order Runge–Kutta Discontinuous Galerkin Methods

Journal of Computational Physics ◽

10.1006/jcph.2001.6718 ◽

2001 ◽

Vol 169 (1) ◽

pp. 111-150 ◽

Author(s):

A. Burbeau ◽

P. Sagaut ◽

Ch.-H. Bruneau

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

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High order central WENO-Implicit-Explicit Runge Kutta schemes for the BGK model on general polygonal meshes

Journal of Computational Physics ◽

10.1016/j.jcp.2020.109766 ◽

2020 ◽

Vol 422 ◽

pp. 109766 ◽

Author(s):

Walter Boscheri ◽

Giacomo Dimarco

Keyword(s):

Bgk Model ◽

Polygonal Meshes ◽

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High order sign-preserving and well-balanced exponential Runge-Kutta discontinuous Galerkin methods for the shallow water equations with friction

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110543 ◽

2021 ◽

pp. 110543

Author(s):

Ruize Yang ◽

Yang Yang ◽

Yulong Xing

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

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High order semi-Lagrangian discontinuous Galerkin method coupled with Runge-Kutta exponential integrators for nonlinear Vlasov dynamics

Journal of Computational Physics ◽

10.1016/j.jcp.2020.110036 ◽

2021 ◽

Vol 427 ◽

pp. 110036

Author(s):

Xiaofeng Cai ◽

Sebastiano Boscarino ◽

Jing-Mei Qiu

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Exponential Integrators ◽

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Runge-Kutta Discontinuous Galerkin Method Using Weno-Type Limiters: Three-Dimensional Unstructured Meshes

Communications in Computational Physics ◽

10.4208/cicp.300810.240511a ◽

2012 ◽

Vol 11 (3) ◽

pp. 985-1005 ◽

Author(s):

Jun Zhu ◽

Jianxian Qiu

Keyword(s):

Discontinuous Galerkin ◽

Hyperbolic Conservation Laws ◽

Three Dimensional ◽

Unstructured Meshes ◽

Finite Volume Methods ◽

High Order Accuracy ◽

Hyperbolic Conservation ◽

Runge Kutta ◽

Nonlinear Hyperbolic Conservation Laws

AbstractThis paper further considers weighted essentially non-oscillatory (WENO) and Hermite weighted essentially non-oscillatory (HWENO) finite volume methods as limiters for Runge-Kutta discontinuous Galerkin (RKDG) methods to solve problems involving nonlinear hyperbolic conservation laws. The application discussed here is the solution of 3-D problems on unstructured meshes. Our numerical tests again demonstrate this is a robust and high order limiting procedure, which simultaneously achieves high order accuracy and sharp non-oscillatory shock transitions.

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