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We present an energy-stable scheme for simulating the incompressible Navier-Stokes equations based on the generalized Positive Auxiliary Variable (gPAV) framework. In the gPAV-reformulated system the original nonlinear term is replaced by a…

Computational Physics · Physics 2020-07-15 L. Lin , N. Ni , Z. Yang , S. Dong

We investigate interfacial fluid dynamics and heat transfer at nanoscales using an improved diffuse interface approach for liquid-vapor interfaces in non-equilibrium. Conventional Navier-Stokes-Korteweg (NSK) formulations often fail to…

Fluid Dynamics · Physics 2026-03-11 Rahul Bhattacharjee , Henning Struchtrup , Anirudh Singh Rana

We present a new numerical scheme for solving the advection equation and its application to Vlasov simulations. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent…

Computational Physics · Physics 2011-07-06 Takashi Minoshima , Yosuke Matsumoto , Takanobu Amano

We study the dynamics of a liquid droplet inside a gas over a large range of the Knudsen numbers. The moving liquid droplet is modeled by the incompressible Navier-Stokes equations, the surrounding rarefied gas by the Boltzmann equation.…

Numerical Analysis · Mathematics 2012-02-15 Sudarshan Tiwari , Axel Klar , Steffen Hardt

An exact and efficient new method to simulate dynamics in dissipative quantum systems is presented. A stochastic Liouville equation, deduced from Feynman and Vernon's path-integral expression of the reduced density matrix, is used to…

Statistical Mechanics · Physics 2009-10-31 J. Stockburger , C. H. Mak

Flow past a low pressure turbine blade in a cascade at $Re \approx 52000$ and angle of incidence $\alpha = 45.5^{0}$ is solved using a code developed in-house for solving 3D compressible Navier-Stokes equations. This code, named ANUROOP,…

Fluid Dynamics · Physics 2016-11-30 Rajesh Ranjan , S M Deshpande , Roddam Narasimha

A number of physical processes in laser-plasma interaction can be described with the two-fluid plasma model. We report on a solver for the three-dimensional two-fluid plasma model equations. This solver is particularly suited for simulating…

Plasma Physics · Physics 2021-02-26 B. Morel , R. Giust , K. Ardaneh , F Courvoisier

We present an efficient and accurate energy-conserving implicit particle-in-cell~(PIC) algorithm for the electrostatic Vlasov system, with particular emphasis on its high robustness for simulating complex plasma systems with multiple…

Computational Physics · Physics 2022-11-21 Zhuoning Li , Zhenli Xu , Zhiguo Yang

The Navier-Stokes equations are paradigmatic equations describing hydrodynamics of an interacting system with microscopic interactions encoded in transport coefficients. In this work we show how the Navier-Stokes equations arise from the…

Statistical Mechanics · Physics 2025-02-05 Maciej Łebek , Miłosz Panfil

In this paper, we investigate numerically a diffuse interface model for the Navier-Stokes equation with fluid-fluid interface when the fluids have different densities \cite{Lowengrub1998}. Under minor reformulation of the system, we show…

Mathematical Physics · Physics 2015-06-18 Zhenlin Guo , Ping Lin , John S. Lowengrub

A semi-implicit, residual-based variational multiscale (VMS) formulation is developed for the incompressible Navier--Stokes equations. The approach linearizes convection using an extrapolated (Oseen-type) convecting velocity, producing a…

We carry out a rigorous error analysis of the first-order semi-discrete (in time) consistent splitting scheme coupled with a generalized scalar auxiliary variable (GSAV) approach for the Navier-Stokes equations with no-slip boundary…

Numerical Analysis · Mathematics 2023-01-05 Xiaoli Li , Jie Shen

We report on the algorithms and numerical methods used in Viriato, a novel fluid-kinetic code that solves two distinct sets of equations: (i) the Kinetic Reduced Electron Heating Model (KREHM) equations [Zocco & Schekochihin, Phys. Plasmas…

Plasma Physics · Physics 2017-07-26 N. F. Loureiro , W. Dorland , L. Fazendeiro , A. Kanekar , A. Mallet , M. S. Vilelas , A. Zocco

Modeling plasma accelerators is a computationally challenging task and the quasi-static particle-in-cell algorithm is a method of choice in a wide range of situations. In this work, we present the first performance-portable, quasi-static,…

We describe a new electrostatic Particle-In-Cell (PIC) code in curvilinear geometry called Curvilinear PIC (CPIC). The code models the microscopic (kinetic) evolution of a plasma with the PIC method, coupled with an adaptive computational…

The Navier-Stokes equations describe the motion of viscous fluids. In order to predict turbulent flows with reasonable computational time and accuracy, these equations are spatially filtered according to the large-eddy simulation (LES)…

Fluid Dynamics · Physics 2018-07-02 Larissa B. Streher , Maurits H. Silvis , Roel Verstappen

This work is devoted to the numerical simulation of a Vlasov-Poisson model describing a charged particle beam under the action of a rapidly oscillating external electric field. We construct an Asymptotic Preserving numerical scheme for this…

Numerical Analysis · Mathematics 2015-06-11 Nicolas Crouseilles , Mohammed Lemou , Florian Méhats

We consider an alternative Navier-Stokes model for compressible viscous ideal gases, originally proposed in \cite{Svard18}. We derive a priori estimates that are sufficiently strong to support a weak entropy solution of the system. Guided…

Numerical Analysis · Mathematics 2022-03-07 Magnus Svärd

We study a model of a general compressible viscous fluid subject to the Coulomb friction law boundary condition. For this model, we introduce a dissipative formulation and prove the existence of dissipative solutions. The proof of this…

Analysis of PDEs · Mathematics 2024-02-22 Sarka Necasova , Justyna Ogorzaly , Jan Scherz

Particle-in-Cell (PIC) simulation codes have wide applicability to first-principles modeling of multidimensional nonlinear plasma phenomena, including wake-field accelerators. This review addresses both finite difference and pseudo-spectral…

Plasma Physics · Physics 2014-08-07 Brendan B. Godfrey