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This paper introduces a memory-reduction third-order compact gas-kinetic scheme (CGKS) for solving compressible Euler and Navier-Stokes equations on 3D unstructured meshes. The scheme utilizes a time-evolution gas distribution function to…

Numerical Analysis · Mathematics 2024-08-21 Hongyu Liu , Xing Ji , Yunpeng Mao , Zhe Qian , Kun Xu

Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional…

Discontinuous Galerkin methods of higher order are applied as temporal discretizations for the transient Navier--Stokes equations. The spatial discretization based on inf-sup stable pairs of finite element spaces is stabilised using a…

Numerical Analysis · Mathematics 2019-10-29 Naveed Ahmed , Gunar Matthies

The Active Flux scheme is a Finite Volume scheme with additional degrees of freedom. It makes use of a continuous reconstruction and does not require a Riemann solver. An evolution operator is used for the additional degrees of freedom on…

Computational Engineering, Finance, and Science · Computer Science 2023-03-14 Oliviu Şugar-Gabor

A convenient approach to derive simple expressions for properties of Stokes flows with low levels of slip is presented. The method is based on a series expansion of a Stokes-flow solution (one satisfying a Navier slip boundary condition)…

Fluid Dynamics · Physics 2025-01-28 Duncan A. Lockerby

We propose and analyze computationally a new fictitious domain method, based on higher order space-time finite element discretizations, for the simulation of the nonstationary, incompressible Navier-Stokes equations on evolving domains. The…

Numerical Analysis · Mathematics 2022-06-22 Mathias Anselmann , Markus Bause

This paper deals with fast simulations of the haemodynamics in large arteries by considering a reduced model of the associated fluid-structure interaction problem, which in turn allows an additional reduction in terms of the numerical…

Numerical Analysis · Mathematics 2018-01-19 Claudia M. Colciago , Simone Deparis

This paper is concerned with the problem of shape optimization of two-dimensional flows governed by the time-dependent Navier-Stokes equations. We derive the structures of shape gradients with respect to the shape of the variable domain for…

Optimization and Control · Mathematics 2007-05-23 Zhiming Gao , Yichen Ma , Hongwei Zhuang

We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…

Numerical Analysis · Mathematics 2024-06-06 Anders Melander , Max E. Bitsch , Dong Chen , Allan P. Engsig-Karup

The Cahn-Hilliard-Navier-Stokes (CHNS) equations represent the fundamental building blocks of hydrodynamic phase-field models for multiphase fluid flow dynamics. Due to the coupling between the Navier-Stokes equation and the Cahn-Hilliard…

Numerical Analysis · Mathematics 2021-07-28 Jia Zhao

This article aims at developing a high order pressure-based solver for the solution of the 3D compressible Navier-Stokes system at all Mach numbers. We propose a cell-centered discretization of the governing equations that splits the fluxes…

Numerical Analysis · Mathematics 2021-03-17 Walter Boscheri , Lorenzo Pareschi

For increasingly rarefied flowfields, the Navier-Stokes (NS) equations lose accuracy partially due to the single temperature approximation. To overcome this barrier, a continuum multi-temperature model based on the Bhatnagar-Gross-Krook…

Fluid Dynamics · Physics 2018-10-12 Guiyu Cao , Hualin Liu , Kun Xu

Reduced order models play an important role in the design, optimization and control of dynamical systems. In recent years, there has been an increasing interest in the application of data-driven techniques for model reduction that can…

Fluid Dynamics · Physics 2021-02-23 Carlos J. G. Rojas , Andreas Dengel , Mateus Dias Ribeiro

We consider two-level finite element discretization methods for the stream function formulation of the Navier-Stokes equations. The two-level method consists of solving a small nonlinear system on the coarse mesh, then solving a linear…

Numerical Analysis · Mathematics 2025-10-20 Faisal Fairag

We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…

Numerical Analysis · Mathematics 2020-02-11 Alexander Zaitzeff , Selim Esedoglu , Krishna Garikipati

We consider settings for which one needs to perform multiple flow simulations based on the Navier-Stokes equations, each having different values for the physical parameters and/or different initial condition data, boundary conditions data,…

Numerical Analysis · Mathematics 2017-06-14 Max Gunzburger , Nan Jiang , Zhu Wang

Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…

Mathematical Physics · Physics 2025-06-06 Ricardo Costa , Stéphane Clain , Gaspar J. Machado , João M. Nóbrega

The boundary layer represents a fundamental structure in fluid dynamics, where accurate boundary discretization significantly enhances computational efficiency. This paper presents a third-order boundary discretization for compact…

Numerical Analysis · Mathematics 2025-03-07 Jiawang Zhang , Xing Ji , Kun Xu

In the preceding paper, linear response methods have been applied to obtain formally exact expressions for the parameters of Navier-Stokes order hydrodynamics. The analysis there is general, applying to both normal and granular fluids with…

Statistical Mechanics · Physics 2007-05-23 Aparna Baskaran , James W. Dufty , J. Javier Brey

A novel fifth-order compact gas-kinetic scheme is developed for high-resolution simulation of compressible flows on structured meshes. Its accuracy relies on a new multidimensional fifth-order compact reconstruction that uses line-averaged…

Numerical Analysis · Mathematics 2025-08-13 Yaqing Yang , Fengxiang Zhao , Kun Xu