English
Related papers

Related papers: An implicit $ P $-multigrid flux reconstruction me…

200 papers

We propose to accelerate a high order discontinuous Galerkin solver using neural networks. We include a corrective forcing to a low polynomial order simulation to enhance its accuracy. The forcing is obtained by training a deep fully…

Fluid Dynamics · Physics 2024-01-10 Fernando Manrique de Lara , Esteban Ferrer

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration…

Numerical Analysis · Mathematics 2017-08-15 Benjamin Krank , Niklas Fehn , Wolfgang A. Wall , Martin Kronbichler

In this paper, we introduce a novel approach that combines multiresolution (MR) techniques with the flux reconstruction (FR) method to accurately and effciently simulate compressible flows. We achieve further enhancements in effciency…

Fluid Dynamics · Physics 2023-06-21 Yixuan Lian , Jinsheng Cai , Shucheng Pan

In this paper, we present a semi-implicit numerical solver for a first order hyperbolic formulation of two-phase flow with surface tension and viscosity. The numerical method addresses several complexities presented by the PDE system in…

Numerical Analysis · Mathematics 2022-08-12 Simone Chiocchetti , Micheal Dumbser

Numerical simulation of incompressible fluid flows has been an active topic of research in Scientific Computing for many years, with many contributions to both discretizations and linear and nonlinear solvers. In this work, we propose an…

Numerical Analysis · Mathematics 2025-12-16 Amin Rafiei , Scott MacLachlan

For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on the time…

Numerical Analysis · Mathematics 2024-03-04 Yaqing Yang , Liang Pan , Kun Xu

A highly efficient gas-kinetic scheme with fourth-order accuracy in both space and time is developed for the Navier-Stokes equations on triangular meshes. The scheme combines an efficient correction procedure via reconstruction (CPR)…

Numerical Analysis · Mathematics 2020-10-20 Chao Zhang , Qibing Li , Z. J. Wang , Jiequan Li , Song Fu

Solving the reactive low-Mach Navier-Stokes equations with high-order adaptive methods in time is still a challenging problem, in particular due to the handling of the algebraic variables involved in the mass constraint. We focus on the…

Analysis of PDEs · Mathematics 2025-10-02 Laurent François , Joël Dupays , Dmitry Davidenko , Marc Massot

An immersed-boundary method for the incompressible Navier--Stokes equations is presented. It employs discrete forcing for a sharp discrimination of the solid-fluid interface, and achieves second-order accuracy, demonstrated in examples with…

We present a high-order implicit large-eddy simulation (ILES) approach for simulating transitional turbulent flows. The approach consists of an Interior Embedded Discontinuous Galerkin (IEDG) method for the discretization of the…

Fluid Dynamics · Physics 2016-05-04 Pablo Fernandez , Ngoc-Cuong Nguyen , Xevi Roca , Jaime Peraire

Most research on preconditioners for time-dependent PDEs has focused on implicit multi-step or diagonally-implicit multi-stage temporal discretizations. In this paper, we consider monolithic multigrid preconditioners for fully-implicit…

Numerical Analysis · Mathematics 2023-02-28 Razan Abu-Labdeh , Scott MacLachlan , Patrick E. Farrell

High-order adaptive time-stepping algorithms are of significant practical value and theoretical interest for accelerating long-time fluid-flow simulations and resolving complex dynamical behaviors. While several high-order implicit-explicit…

Numerical Analysis · Mathematics 2026-05-08 Hong-lin Liao , Xiaoming Wang , Xuping Wang , Cao Wen

We propose a new arbitrary high order accurate semi-implicit space-time discontinuous Galerkin (DG) method for the solution of the two and three dimensional compressible Euler and Navier-Stokes equations on staggered unstructured curved…

Numerical Analysis · Mathematics 2017-05-24 Maurizio Tavelli , Michael Dumbser

We consider high order, implicit Runge-Kutta schemes to solve time-dependent stiff PDEs on dynamically adapted grids generated by multiresolution analysis for unsteady problems disclosing localized fronts. The multiresolution finite volume…

Numerical Analysis · Mathematics 2016-04-04 Max Duarte , Richard Dobbins , Mitchell Smooke

We present a novel fully implicit hybrid finite volume/finite element method for incompressible flows. Following previous works on semi-implicit hybrid FV/FE schemes, the incompressible Navier-Stokes equations are split into a pressure and…

Numerical Analysis · Mathematics 2023-02-14 Alessia Lucca , Saray Busto , Michael Dumbser

In this work, we detail the GPU-porting of an in-house pseudo-spectral solver tailored towards large-scale simulations of interface-resolved simulation of drop- and bubble-laden turbulent flows. The code relies on direct numerical…

Fluid Dynamics · Physics 2024-06-04 Alessio Roccon

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the…

Fluid Dynamics · Physics 2017-01-04 Sebastian Liska , Tim Colonius

Computational fluid dynamics (CFD) simulations of viscous fluids described by the Navier-Stokes equations are considered. Depending on the Reynolds number of the flow, the Navier-Stokes equations may exhibit a highly nonlinear behavior. The…

Numerical Analysis · Mathematics 2023-10-11 Anouk Zandbergen , Tycho van Noorden , Alexander Heinlein

High-order nodal space-time flux reconstruction (STFR) methods have been developed to solve hyperbolic conservation laws on curvilinear moving grids. Unlike the method-of-lines approach for moving domain simulation, the grid velocity is…

Numerical Analysis · Mathematics 2025-11-19 Meilin Yu

An a priori reduced order method based on the proper generalised decomposition (PGD) is proposed to compute parametric solutions involving turbulent incompressible flows of interest in an industrial context, using OpenFOAM. The PGD…

Computational Physics · Physics 2021-11-16 Vasileios Tsiolakis , Matteo Giacomini , Ruben Sevilla , Carsten Othmer , Antonio Huerta