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We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method…

Fluid Dynamics · Physics 2025-08-22 Xinjie Ji , Changxiao Nigel Shen , Wim M. van Rees

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured triangular…

Numerical Analysis · Mathematics 2014-12-04 Maurizio Tavelli , Michael Dumbser

In this paper, a third-order compact gas-kinetic scheme (GKS) on unstructured tetrahedral mesh is constructed for the compressible Euler and Navier-Stokes solutions. The time-dependent gas distribution function at a cell interface is used…

Computational Physics · Physics 2021-02-03 Xing Ji , Fengxiang Zhao , Wei Shyy , Kun Xu

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

A new fourth order compact formulation for the steady 2-D incompressible Navier-Stokes equations is presented. The formulation is in the same form of the Navier-Stokes equations such that any numerical method that solve the Navier-Stokes…

Numerical Analysis · Mathematics 2025-10-20 E. Erturk , C. Gokcol

This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined Cartesian grids that adapt to the evolving interfaces and track regions of high vorticity. The…

Computational Physics · Physics 2019-09-04 Nishant Nangia , Boyce E. Griffith , Neelesh A. Patankar , Amneet Pal Singh Bhalla

In this work, we report the development of a spatially fourth order temporally second order compact scheme for incompressible Navier-Stokes (N-S) equations in time-varying domain. Sen [J. Comput. Phys. 251 (2013) 251-271] put forward an…

Numerical Analysis · Mathematics 2021-08-26 Shuvam Sen , Tony W. H. Sheu

A dual time-stepping strategy of gas-kinetic scheme for the simulation of unsteady flows is introduced in this work. The dual time-stepping strategy is always used in the approaches of unsteady flows, and the ability of dual time-stepping…

Fluid Dynamics · Physics 2017-05-31 Ji Li , Chengwen Zhong , Yong Wang , Congshan Zhuo

The trade-off among accuracy, robustness, and computational cost remains a key challenge in simulating complex flows. Second-order schemes are computationally efficient but lack the accuracy required for resolving intricate flow structures,…

Numerical Analysis · Mathematics 2025-08-28 Yaqing Yang , Fengxiang Zhao , Kun Xu

We develop a $ P $-multigrid solver to simulate locally preconditioned unsteady compressible Navier-Stokes equations at low Mach numbers with implicit high-order methods. Specifically, the high-order flux reconstruction/correction procedure…

Computational Physics · Physics 2019-08-13 Lai Wang , Meilin Yu

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

We present a fully-coupled, implicit-in-time framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes system that models two-phase flows. In this work, we extend the block iterative method presented in Khanwale et…

In this paper, we propose a Runge-Kutta (RK) central discontinuous Galerkin (CDG) gas-kinetic BGK method for the Navier-Stokes equations. The proposed method is based on the CDG method defined on two sets of overlapping meshes to avoid…

Numerical Analysis · Mathematics 2015-06-18 Tan Ren , Jun Hu , Tao Xiong , Jing-Mei Qiu

This paper presents an arbitrary h.o. accurate ADER DG method on space-time adaptive meshes (AMR) for the solution of two important families of non-linear time dependent PDE for compr. dissipative flows: the compr. Navier-Stokes equations…

Numerical Analysis · Mathematics 2021-07-22 Francesco Fambri , Michael Dumbser , Olindo Zanotti

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

A new high order accurate staggered semi-implicit space-time discontinuous Galerkin (DG) method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions. The staggered DG…

Numerical Analysis · Mathematics 2020-10-09 Francesco Lohengrin Romeo , Michael Dumbser , Maurizio Tavelli

We construct first- and second-order time discretization schemes for the Cahn-Hilliard-Navier-Stokes system based on the multiple scalar auxiliary variables approach (MSAV) approach for gradient systems and (rotational) pressure-correction…

Numerical Analysis · Mathematics 2020-09-22 Xiaoli Li , Jie Shen

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

Incompressible flow solvers based on strong-form meshfree methods represent arbitrary geometries without the need for a global mesh system. However, their local evaluations make it difficult to satisfy incompressibility at the discrete…

Numerical Analysis · Mathematics 2026-05-05 Takeharu Matsuda , Satoshi Ii

The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by…

Computational Physics · Physics 2022-11-22 Alejandro Quirós Rodríguez , Tomas Fullana , Vincent Le Chenadec , Taraneh Sayadi