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Development of highly scalable and robust algorithms for large-scale CFD simulations has been identified as one of the key ingredients to achieve NASA's CFD Vision 2030 goals. In order to improve simulation capability and to effectively…

Numerical Analysis · Mathematics 2021-01-07 Zan Xu , Léopold Cambier , Juan J. Alonso , Eric Darve

We present a compatible space-time hybridizable/embedded discontinuous Galerkin discretization for nonlinear free-surface waves. We pose this problem in a two-fluid (liquid and gas) domain and use a time-dependent level-set function to…

Numerical Analysis · Mathematics 2023-07-10 Giselle Sosa Jones , Sander Rhebergen

This paper is concerned with developing accurate and efficient discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in the case of one spatial dimension. The primary…

Numerical Analysis · Mathematics 2012-12-05 Xiaobing Feng , Thomas Lewis

We perform a complete Fourier analysis of the semi-discrete 1-d wave equation obtained through a P1 discontinuous Galerkin (DG) approximation of the continuous wave equation on an uniform grid. The resulting system exhibits the interaction…

Analysis of PDEs · Mathematics 2010-08-03 Aurora-Mihaela Marica , Enrique Zuazua

We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…

Numerical Analysis · Mathematics 2020-01-08 Hong Xiao , Eky Febrianto , Qiaoling Zhang , Fehmi Cirak

In this contribution we present a local discontinuous Galerkin (LDG) pressure-correction scheme for the incompressible Navier-Stokes equations. The scheme does not need penalty parameters and satisfies the discrete continuity equation…

Numerical Analysis · Mathematics 2020-03-30 Janick Thomas Gerstenberger , Samuel Burbulla , Dietmar Kröner

A wall-modeled large eddy simulation approach is proposed in a Discontinuous Galerkin (DG) setting, building on the slip-wall concept of Bae et al. (JFM'19) and the universal scaling relationship by Pradhan and Duraisamy (JFM'23). The…

Fluid Dynamics · Physics 2025-04-25 Pratikkumar Raje , Karthik Duraisamy

This paper considers the discontinuous Galerkin (DG) methods for solving the Vlasov-Maxwell (VM) system, a fundamental model for collisionless magnetized plasma. The DG methods provide accurate numerical description with conservation and…

Numerical Analysis · Mathematics 2022-10-17 Andrés Galindo-Olarte , Juntao Huang , Jennifer K. Ryan , Yingda Cheng

We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…

Numerical Analysis · Mathematics 2022-10-26 Siyang Wang , Gunilla Kreiss

The study performs large-eddy simulations of supersonic free jet flows using the Discontinuous Galerkin Spectral Element Method (DGSEM). The main objective of the present work is to assess the resolution requirements for adequate simulation…

Fluid Dynamics · Physics 2024-03-22 Diego F. Abreu , João Luiz F. Azevedo , Carlos Junqueira-Junior

In the first part of this paper, uniqueness of strong solution is established for the Vlasov-unsteady Stokes problem in 3D. The second part deals with a semi discrete scheme, which is based on the coupling of discontinuous Galerkin…

Numerical Analysis · Mathematics 2024-12-17 Harsha Hutridurga , Krishan Kumar , Amiya K. Pani

Entropy stable discontinuous Galerkin (DG) methods improve the robustness of high order DG simulations of nonlinear conservation laws. These methods yield a semi-discrete entropy inequality, and rely on an algebraic flux differencing…

Numerical Analysis · Mathematics 2025-07-03 Jesse Chan

We present the two-dimensional unstructured grids extension of the a posteriori local subcell correction of discontinuous Galerkin (DG) schemes introduced in [52]. The technique is based on the reformulation of DG scheme as a finite volume…

Numerical Analysis · Mathematics 2022-12-23 François Vilar , Rémi Abgrall

This work develops a robust and efficient framework of the adjoint gradient-based aerodynamic shape optimization (ASO) using high-order discontinuous Galerkin methods (DGMs) as the CFD solver. The adjoint-enabled gradients based on…

Numerical Analysis · Mathematics 2024-07-30 Yiwei Feng , Lili Lv , Tiegang Liu , Kun Wang , Bangcheng Ai

Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…

Numerical Analysis · Mathematics 2021-01-25 Andrea Barth , Andreas Stein

For a class of fourth order gradient flow problems, integration of the scalar auxiliary variable (SAV) time discretization with the penalty-free discontinuous Galerkin (DG) spatial discretization leads to SAV-DG schemes. These schemes are…

Numerical Analysis · Mathematics 2020-08-28 Hailiang Liu , Peimeng Yin

In recent years several research efforts focused on the development of high-order discontinuous Galerkin (dG) methods for scale resolving simulations of turbulent flows. Nevertheless, in the context of incompressible flow computations, the…

Computational Physics · Physics 2019-05-14 Matteo Franciolini , Lorenzo Botti , Alessandro Colombo , Andrea Crivellini

Grad-div stabilization is a classical remedy in conforming mixed finite element methods for incompressible flow problems, for mitigating velocity errors that are sometimes called poor mass conservation. Such errors arise due to the…

Numerical Analysis · Mathematics 2019-04-12 Mine Akbas , Alexander Linke , Leo G. Rebholz , Philipp W. Schroeder

The application of discontinuous Galerkin (DG) schemes to hyperbolic systems of conservation laws requires a careful interplay between space discretization, carried out with local polynomials and numerical fluxes at inter-cells, and…

Numerical Analysis · Mathematics 2025-11-11 Maya Briani , Gabriella Puppo , Giuseppe Visconti

In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For the purpose of numerics, the Green-Naghdi model is rewritten into…

Numerical Analysis · Mathematics 2019-10-23 Maojun Li , Liwei Xu , Yongping Cheng