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In this paper, a high-order gas-kinetic scheme in general curvilinear coordinate (HGKS-cur) is developed for the numerical simulation of compressible turbulence. Based on the coordinate transformation, the Bhatnagar-Gross-Krook (BGK)…

Fluid Dynamics · Physics 2021-07-20 Guiyu Cao , Kun Xu , Liang Pan , Minping Wan , Shiyi Chen

The pressure-correction method is a well established approach for simulating unsteady, incompressible fluids. It is well-known that implicit discretization of the time derivative in the momentum equation e.g. using a backward…

Numerical Analysis · Mathematics 2024-07-17 Utku Kaya , Thomas Richter

In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…

Numerical Analysis · Mathematics 2020-11-02 Chen Liu , Deep Ray , Christopher Thiele , Lu Lin , Beatrice Riviere

Compact Runge-Kutta (cRK) Flux Reconstruction (FR) methods are a variant of RKFR methods for hyperbolic conservation laws with a compact stencil including only immediate neighboring finite elements. We extend cRKFR methods to handle…

Numerical Analysis · Mathematics 2025-12-10 Arpit Babbar , Hendrik Ranocha

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

Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to…

Computational Engineering, Finance, and Science · Computer Science 2020-07-15 Chennakesava Kadapa , Wulf G Dettmer , Djordje Peric

We present a dynamically load-balanced parallel $ p $-adaptive implicit high-order flux reconstruction method for under-resolved turbulence simulation. The high-order explicit first stage, singly diagonal implicit Runge-Kutta (ESDIRK)…

Computational Physics · Physics 2020-07-15 Lai Wang , Matthias K. Gobbert , Meilin Yu

A computationally accurate and efficient numerical method under a unified framework is crucial to various multi-scale scientific and engineering problems. So far, many numerical methods have encountered various challenges in efficiently…

Fluid Dynamics · Physics 2023-03-21 Rui Zhang , Sha Liu , Jianfeng Chen , Chengwen Zhong , Congshan Zhuo

We present a linear, second order fully discrete numerical scheme on a staggered grid for a thermodynamically consistent hydrodynamic phase field model of binary compressible fluid flow mixtures derived from the generalized Onsager…

Numerical Analysis · Mathematics 2019-07-24 Xueping Zhao , Qi Wang

This work aims to introduce a heuristic timestep-adaptive algorithm for Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems where the flow is dominated by the pressure. In such scenarios, many time-adaptive…

Numerical Analysis · Mathematics 2024-07-02 Ivan Prusak , Davide Torlo , Monica Nonino , Gianluigi Rozza

The inability of the Navier-Stokes-Fourier equations to capture rarefaction effects motivates us to adopt the extended hydrodynamic equations. In the present work, a hydrodynamic model, which consists of the conservation laws closed with…

Fluid Dynamics · Physics 2023-08-25 Himanshi , Anirudh Singh Rana , Vinay Kumar Gupta

We present a high-order method for flow simulation on unstructured curved nonconforming sliding meshes. This method utilizes dynamic transfinite mortar elements to exchange flow information between the two sides of a sliding interface. The…

Numerical Analysis · Mathematics 2021-07-28 Bin Zhang , Chunlei Liang

Solving compressible flows containing both smooth and discontinuous flow structures remains a significant challenge for finite volume methods. Godunov-type finite volume methods are commonly used for numerical simulations of compressible…

Fluid Dynamics · Physics 2025-02-07 Minsheng Huang , Lidong Cheng , Wenjun Ying , Xi Deng , Feng Xiao

We present a novel structure-preserving semi-implicit finite volume method on vertex-based staggered meshes for the compatible discretization of first order systems of time-dependent partial differential equations (PDEs). The method…

Numerical Analysis · Mathematics 2026-04-24 Elena Bernardelli , Elena Gaburro , Michael Dumbser

In fluid physics, data-driven models to enhance or accelerate solution methods are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In…

We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent…

Fluid Dynamics · Physics 2018-08-16 Tharindu P. Miyanawala , Rajeev K. Jaiman

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

We present an Asymptotic-Preserving 'all-speed' scheme for the simulation of compressible flows valid at all Mach-numbers ranging from very small to order unity. The scheme is based on a semi-implicit discretization which treats the…

Mathematical Physics · Physics 2014-04-08 Floraine Cordier , Pierre Degond , Anela Kumbaro

Continuing on our previous work [ArXiv:1212.2644], we develop semi-implicit numerical methods for solving low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with…

Numerical Analysis · Mathematics 2016-01-20 A. J. Nonaka , Y. Sun , J. B. Bell , A. Donev

In this paper we present a novel pressure-based semi-implicit finite volume solver for the equations of compressible ideal, viscous and resistive magnetohydrodynamics (MHD). The new method is conservative for mass, momentum and total energy…

Numerical Analysis · Mathematics 2018-12-26 Michael Dumbser , Dinshaw S. Balsara , Maurizio Tavelli , Francesco Fambri