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Related papers: A two-stage fourth-order gas-kinetic CPR method fo…

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This study proposes an extension of the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulation in an arbitrary Lagrangian-Eulerian (ALE) formulation in unstructured mesh. The ALE method is achieved by subdividing…

Computational Physics · Physics 2024-01-05 Yue Zhang , Kun Xu

We present a fourth-order projection method with adaptive mesh refinement (AMR) for numerically solving the incompressible Navier-Stokes equations (INSE) with subcycling in time. Our method features (i) a reformulation of INSE so that the…

Numerical Analysis · Mathematics 2025-09-08 Shubo Zhao , Qinghai Zhang

We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…

Numerical Analysis · Mathematics 2023-12-29 Gauthier Wissocq , Rémi Abgrall

In this paper, a unified gas kinetic scheme for multiphase dilute gas-particle system is proposed. The UGKS multiphase (UGKS-M) is a finite volume method, which captures flow physics in the regimes from collisionless multispecies transport…

Computational Physics · Physics 2019-05-01 Chang Liu , Zhao Wang , Kun Xu

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

This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…

Numerical Analysis · Mathematics 2019-02-01 Victor DeCaria , William Layton , Haiyun Zhao

We analyze the representation of viscous stresses in the one-fluid formulation of the two-phase Navier-Stokes equations, the model on which all computational approaches making use of a fixed mesh to discretize the flow field are grounded.…

Fluid Dynamics · Physics 2025-06-06 Jacques Magnaudet , Hadrien Bruhier , Samuel Mer , Thomas Bonometti

The Cahn-Hilliard Navier-Stokes (CHNS) system provides a computationally tractable model that can be used to effectively capture interfacial dynamics in two-phase fluid flows. In this work, we present a semi-implicit, projection-based…

Accurate prediction of rarefied gas flows is important for space vehicle design, particularly in rarefied regimes where the Navier-Stokes equations are no more valid. While the direct simulation Monte Carlo (DSMC) method acts as a numerical…

Fluid Dynamics · Physics 2025-07-01 Joonbeom Kim , Eunji Jun

Fluid simulations are often performed using the incompressible Navier-Stokes equations (INSE), leading to sparse linear systems which are difficult to solve efficiently in parallel. Recently, kinetic methods based on the…

Graphics · Computer Science 2021-01-29 Yixin Chen , Wei Li , Rui Fan , Xiaopei Liu

The well-known Navier--Stokes--Fourier equations of fluid dynamics are, in general, not adequate for describing rarefied gas flows. Moreover, while the Stokes equations -- a simplified version of the Navier--Stokes--Fourier equations -- are…

Fluid Dynamics · Physics 2025-03-21 Himanshi , Anirudh Singh Rana , Vinay Kumar Gupta

This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is…

Numerical Analysis · Mathematics 2022-02-02 Jean-Luc Guermond , Martin Kronbichler , Matthias Maier , Bojan Popov , Ignacio Tomas

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

As an extension of previous fourth-order compact gas kinetic scheme (GKS) on structured meshes (Ji et al. 2018), this work is about the development of a third-order compact GKS on unstructured meshes for the compressible Euler and…

Computational Physics · Physics 2019-02-15 Xing Ji , Fengxiang Zhao , Wei Shyy , Kun Xu

A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation sys-tem in this paper. Variable densities and viscosities are considered in the nu-merical scheme.…

Computational Physics · Physics 2018-05-25 Xiaoyu Feng , Jisheng Kou , Shuyu Sun

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 paper, a third order gas kinetic scheme is developed on the three dimensional hybrid unstructured meshes for the numerical simulation of compressible inviscid and viscous flows. A third-order WENO reconstruction is developed on the…

Numerical Analysis · Mathematics 2022-04-18 Yaqing Yang , Liang Pan , Kun Xu

This study presents an efficient and accurate discrete adjoint gas-kinetic scheme (GKS) for sensitivity analysis and aerodynamic shape optimization in continuum flow regimes. Developed using the backward mode of algorithmic differentiation…

Fluid Dynamics · Physics 2026-04-17 Hangkong Wu , Yuze Zhu , Yajun Zhu , Kun Xu

We study periodic solutions to the Navier-Stokes equations. The transition phase of a dynamic Navier-Stokes solution to the periodic-in-time state can be excessively long and it depends on parameters like the domain size and the viscosity.…

Numerical Analysis · Mathematics 2019-12-30 Thomas Richter

In this paper an even higher-order compact GKS up to sixth order of accuracy will be constructed for the shock and acoustic wave computation on unstructured mesh. The compactness is defined by the physical domain of dependence for an…

Numerical Analysis · Mathematics 2020-10-20 Fengxiang Zhao , Xing Ji , Wei Shyy , Kun Xu