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The computational cost of fluid simulations increases rapidly with grid resolution. This has given a hard limit on the ability of simulations to accurately resolve small scale features of complex flows. Here we use a machine learning…

Computational Physics · Physics 2021-06-23 Jiawei Zhuang , Dmitrii Kochkov , Yohai Bar-Sinai , Michael P. Brenner , Stephan Hoyer

A specialized mesh-free radial basis function-based finite difference (RBF-FD) discretization is used to solve the large eigenvalue problems arising in hydrodynamic stability analyses of flows in complex domains. Polyharmonic spline…

Fluid Dynamics · Physics 2023-08-15 Tianyi Chu , Oliver T. Schmidt

Turbulent flow has been extensively studied using computational fluid dynamics (CFD) simulations since turbulent flow regime is so frequently encountered in both academic and engineering applications. The high-fidelity simulation of the…

Fluid Dynamics · Physics 2024-05-21 Minghan Chu

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

We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder that exhibits chaotic behavior, to examine the behavior of various numerical methods. We choose a range of Reynolds numbers for which the flow is…

Numerical Analysis · Mathematics 2024-08-19 Henry von Wahl , L. Ridgway Scott

The two-fluid plasma equations for a single ion species, with full transport terms, including temperature and magnetic field dependent ion and electron viscous stresses and heat fluxes, frictional drag force, and ohmic heating term have…

Plasma Physics · Physics 2019-02-04 Z. Li , D. Livescu

Particle-in-cell methods with stochastic collision models are commonly used to simulate collisional plasma dynamics, with applications ranging from hypersonic flight to semiconductor manufacturing. Code verification of such methods is…

Computational Physics · Physics 2026-05-26 Brian A. Freno , William J. McDoniel , Christopher H. Moore , Neil R. Matula

The Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) method is a Lagrangian method that is typically used for the simulation of incompressible fluids. While developing an SPH-based scheme or solver, researchers often verify their…

Fluid Dynamics · Physics 2022-01-14 Pawan Negi , Prabhu Ramachandran

Physical systems are governed by partial differential equations (PDEs). The Navier-Stokes equations describe fluid flows and are representative of nonlinear physical systems with complex spatio-temporal interactions. Fluid flows are…

Fluid Dynamics · Physics 2022-10-05 Deniz A. Bezgin , Aaron B. Buhendwa , Nikolaus A. Adams

Mesh-free methods have significant potential for simulations of flows in complex geometries, with the difficulties of domain discretisation greatly reduced. However, many mesh-free methods are limited to low order accuracy. In order to…

Fluid Dynamics · Physics 2021-11-10 Jack King , Steven Lind

Simulation of turbulent flows at high Reynolds number is a computationally challenging task relevant to a large number of engineering and scientific applications in diverse fields such as climate science, aerodynamics, and combustion.…

Computational Physics · Physics 2020-10-06 Jaideep Pathak , Mustafa Mustafa , Karthik Kashinath , Emmanuel Motheau , Thorsten Kurth , Marcus Day

A fully implicit high-order preconditioned flux reconstruction/correction procedure via reconstruction (FR/CPR) method is developed to solve the compressible Navier-Stokes equations at low Mach numbers. A dual-time stepping approach with…

Computational Physics · Physics 2019-10-23 Lai Wang , Meilin Yu

The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…

Numerical Analysis · Mathematics 2025-08-12 Dominic Breit , Andreas Prohl , Jörn Wichmann

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

Most high order computational fluid dynamics (CFD) methods for compressible flows are based on Riemann solver for the flux evaluation and Runge-Kutta (RK) time stepping technique for temporal accuracy. The main advantage of this kind of…

Computational Physics · Physics 2018-01-17 Xing Ji , Fengxiang Zhao , Wei Shyy , Kun Xu

The Finite Volume Method in Computational Fluid Dynamics to numerically model a fluid flow problem involves the process of formulating the numerical flux at the faces of the control volume. This process is important in deciding the…

Numerical Analysis · Mathematics 2021-08-05 Osama A. Marzouk

We derive and analyze a broad class of finite element methods for numerically simulating the stationary, low Reynolds number flow of concentrated mixtures of several distinct chemical species in a common thermodynamic phase. The underlying…

Numerical Analysis · Mathematics 2025-09-24 Aaron Baier-Reinio , Patrick E. Farrell

The method of fundamental solutions (MFS) is known to be effective for solving 3D Laplace and Stokes Dirichlet boundary value problems in the exterior of a large collection of simple smooth objects. Here we present new scalable MFS…

Numerical Analysis · Mathematics 2025-08-22 Anna Broms , Alex H. Barnett , Anna-Karin Tornberg

The verification and validation of a high-order compressible in-house solver based on a compact finite difference scheme are presented. Validation is performed using five canonical cases: the one-dimensional Sod shock tube problem,…

Fluid Dynamics · Physics 2026-02-09 Yujoo Kang , Sang Lee

In this paper, we develop a new free-stream preserving (FP) method for high-order upwind conservative finite-difference (FD) schemes on the curvilinear grids. This FP method is constrcuted by subtracting a reference cell-face flow state…

Numerical Analysis · Mathematics 2021-01-18 Hongmin Su , Jinsheng Cai , Shucheng Pan , Xiangyu Hu