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In this paper we propose a new spatially high order accurate semi-implicit discontinuous Galerkin (DG) method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured curved meshes. While the…

Numerical Analysis · Mathematics 2014-07-07 Maurizio Tavelli , Michael Dumbser

In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semiimplicit second-order accuracy in time and spectral accuracy…

In this paper, we are interested in constructing a scheme solving compressible Navier--Stokes equations, with desired properties including high order spatial accuracy, conservation, and positivity-preserving of density and internal energy…

Numerical Analysis · Mathematics 2023-09-13 Chen Liu , Xiangxiong Zhang

We investigate a novel monolithic algebraic multigrid (AMG) preconditioner for the Taylor-Hood ($\pmb{\mathbb{P}}_2/\mathbb{P}_1$) and Scott-Vogelius ($\pmb{\mathbb{P}}_2/\mathbb{P}_1^{disc}$) discretizations of the Stokes equations. The…

Numerical Analysis · Mathematics 2024-09-04 Alexey Voronin , Scott MacLachlan , Luke N. Olson , Raymond Tuminaro

This study proposes an algorithm for modeling compressible flows in spherical shells in nearly incompressible and weakly compressible regimes based on an implicit direction splitting approach. The method retains theoretically expected…

Numerical Analysis · Mathematics 2021-04-21 Roman Frolov , Peter Minev , Aziz Takhirov

We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, we…

Numerical Analysis · Mathematics 2025-04-16 Santolo Leveque , Michele Benzi , Patrick E. Farrell

We present a matrix-free flow solver for high-order finite element discretizations of the incompressible Navier-Stokes and Stokes equations with GPU acceleration. For high polynomial degrees, assembling the matrix for the linear systems…

Numerical Analysis · Mathematics 2020-04-21 Michael Franco , Jean-Sylvain Camier , Julian Andrej , Will Pazner

Efficient simulation of nonlinear and dispersive free-surface flows governed by the incompressible Navier-Stokes equations remains a central challenge in ocean and coastal engineering. The computational bottleneck arises from solving a…

This study proposes a high-efficient machine learning (ML) projection method using forward-generated data for incompressible Navier-Stokes equations. A Poisson neural network (Poisson-NN) embedded method and a wavelet transform…

Fluid Dynamics · Physics 2025-09-03 Ruilin Chen

This work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of…

Computational Physics · Physics 2018-12-14 Matteo Franciolini , Krzysztof Fidkowski , Andrea Crivellini

We present a spectral element model for general-purpose simulation of non-overturning nonlinear water waves using the incompressible Navier-Stokes equations (INSE) with a free surface. The numerical implementation of the spectral element…

Numerical Analysis · Mathematics 2024-11-25 Anders Melander , Wojciech Laskowski , Spencer J. Sherwin , Allan P. Engsig-Karup

In recent years, topology optimization has been developed sufficiently and many researchers have concentrated on enhancing to computationally numerical algorithms for computational effectiveness of this method. Along with the development of…

Numerical Analysis · Mathematics 2023-01-19 Nam G. Luu , Thanh T. Banh

Neumann series underlie both Krylov methods and algebraic multigrid smoothers. A low-synch modified Gram-Schmidt (MGS)-GMRES algorithm is described that employs a Neumann series to accelerate the projection step. A corollary to the backward…

Numerical Analysis · Mathematics 2021-12-30 Stephen Thomas , Arielle Carr , Paul Mullowney , Ruipeng Li , Kasia Świrydowicz

The novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational…

Numerical Analysis · Mathematics 2010-01-20 Matteo Semplice , Marco Donatelli , Stefano Serra-Capizzano

This paper studies inf-sup stable finite element discretizations of the evolutionary Navier--Stokes equations with a grad-div type stabilization. The analysis covers both the case in which the solution is assumed to be smooth and…

Numerical Analysis · Mathematics 2017-05-29 Javier de Frutos , Bosco García-Archilla , Volker John , Julia Novo

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time DG method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As…

Numerical Analysis · Mathematics 2016-06-22 Maurizio Tavelli , Michael Dumbser

The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular…

Numerical Analysis · Mathematics 2016-12-08 Amneet Pal Singh Bhalla , Matthew G. Knepley , Mark F. Adams , Robert D. Guy , Boyce E. Griffith

In this paper we present a numerical method for hydrodynamic models that arise from time dependent density functional theories of freezing. The models take the form of compressible Navier-Stokes equations whose pressure is determined by the…

Numerical Analysis · Mathematics 2016-01-20 Arvind Baskaran , Zhen Guan , John Lowengrub

The paper aims at developing low-storage implicit Runge-Kutta methods which are easy to implement and achieve higher-order of convergence for both the velocity and pressure in the finite volume formulation of the incompressible…

Numerical Analysis · Mathematics 2019-07-08 Jiawei Wan , Ahsan Kareem , Haili Liao , Yunzhu Cai

Numerical simulation of incompressible viscous flow, in particular in three space dimensions, continues to remain a challenging task. Space-time finite element methods feature the natural construction of higher order discretization schemes.…

Numerical Analysis · Mathematics 2022-10-07 Mathias Anselmann , Markus Bause