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We consider a diffuse-interface model for two-phase incompressible viscous flows with a soluble surfactant in a bounded porous medium. This hydrodynamic system consists of a Darcy--Forchheimer equation for the seepage velocity…

Analysis of PDEs · Mathematics 2026-03-24 Maurizio Grasselli , Bohan Ouyang , Andrea Poiatti , Hao Wu

In this paper an approach for decreasing the computational effort required for the split-step Fourier method (SSFM) is introduced. It is shown that using the sparsity property of the simulated signals, the compressive sampling algorithm can…

Computational Physics · Physics 2015-12-15 Cihan Bayindir

A two-stage super-resolution simulation method is proposed for street-scale air temperature and wind velocity, which considerably reduces computation time while maintaining accuracy. The first stage employs a convolutional neural network…

Atmospheric and Oceanic Physics · Physics 2025-01-13 Yuki Yasuda , Ryo Onishi

The semi-analytical wall boundary conditions present a mathematically rigorous framework to prescribe the influence of solid walls in SPH for fluid flows. In this paper they are investigated with respect to the skew-adjoint property which…

Fluid Dynamics · Physics 2015-06-15 Arno Mayrhofer , Benedict D. Rogers , Damien Violeau , Martin Ferrand

In this work, we propose a novel phase-field model for the simulation of two-phase flows that is accurate, conservative, bounded, and robust. The proposed model conserves the mass of each of the phases, and results in bounded transport of…

Computational Physics · Physics 2022-08-23 Suhas S. Jain

In this work we study the solution of the Riemann problem for the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) two-phase flow model introduced in \cite{Romenski2007,Romenski2009}. All…

Analysis of PDEs · Mathematics 2022-11-29 Ferdinand Thein , Evgeniy Romenski , Michael Dumbser

With increasing engineering demands, there need high order accurate schemes embedded with precise physical information in order to capture delicate small scale structures and strong waves with correct "physics". There are two families of…

Numerical Analysis · Mathematics 2018-11-27 Jiequan Li

In this article we consider the numerical modeling and simulation via the phase field approach of two-phase flows of different densities and viscosities in superposed fluid and porous layers. The model consists of the…

Numerical Analysis · Mathematics 2021-12-09 Yali Gao , Daozhi Han , Xiaoming He , Ulrich Rüde

We investigate a model for traffic flow based on the Lighthill-Whitham-Richards model that consists of a hyperbolic conservation law with a discontinuous, piecewise-linear flux. A mollifier is used to smooth out the discontinuity in the…

Numerical Analysis · Mathematics 2013-05-17 Jeffrey K. Wiens , John M. Stockie , JF Williams

The present paper addresses the development and implementation of the first high-order Flux Reconstruction (FR) solver for high-speed flows within the open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid Dynamics)…

Computational Physics · Physics 2019-07-24 Ray Vandenhoeck , Andrea Lani

We consider a real two-fluid system of compressible viscous fluids with a common velocity field and algebraic closure for the pressure law. The constitutive relation involves densities of both fluids through an implicit function. The…

Analysis of PDEs · Mathematics 2026-02-24 Yang Li , Mária Lukáčová-Medvid'ová , Milan Pokorný , Ewelina Zatorska

In this paper, we propose a modification of an acoustic-transport operator splitting Lagrange-projection method for simulating compressible flows with gravity. The original method involves two steps that respectively account for acoustic…

Numerical Analysis · Mathematics 2023-10-30 Rémi Bourgeois , Pascal Tremblin , Samuel Kokh , Thomas Padioleau

The ghost fluid method allows a propagating interface to remain sharp during a numerical simulation. The solution of the Riemann problem at the interface provides proper information to determine interfacial fluxes as well as the velocity of…

Fluid Dynamics · Physics 2023-05-18 Steven Jöns , Christoph Müller , Johanna Hintz , Andrea Beck , Claus-Dieter Munz

This paper proposes an efficient potential and viscous flow decomposition method for wave-structure interaction simulation with single-phase potential flow wave models and two-phase Computational Fluid Dynamics (CFD) solvers. The potential…

We study a non-local version of the Cahn-Hilliard dynamics for phase separation in a two-component incompressible and immiscible mixture with linear mobilities. In difference to the celebrated local model with nonlinear mobility, it is only…

Analysis of PDEs · Mathematics 2019-03-07 Clément Cancès , Daniel Matthes , Flore Nabet

We propose a numerical methodology for the numerical simulation of distinct, interacting physical processes described by a combination of compressible, inert and reactive forms of the Euler equations, multiphase equations and elastoplastic…

Computational Physics · Physics 2018-05-09 Louisa Michael , Nikolaos Nikiforakis

In subsurface multiphase flow simulations, poor nonlinear solver performance is a significant runtime sink. The system of fully implicit mass balance equations is highly nonlinear and often difficult to solve for the nonlinear solver,…

Numerical Analysis · Mathematics 2021-11-24 Sebastian B. M. Bosma , Francois P. Hamon , Brad T. Mallison , Hamdi A. Tchelepi

Simulating compositional multiphase flow in porous media is a challenging task, especially when phase transition is taken into account. The main problem with phase transition stems from the inconsistency of the primary variables such as…

Numerical Analysis · Mathematics 2021-01-08 Q. M. Bui , H. C. Elman

An advanced Volume of Fluid (VOF) method is presented that enables performant three-dimensional Direct Numerical Simulations (DNS) of the interaction of two immiscible fluids in a gaseous environment with large topology changes, e.g.,…

Fluid Dynamics · Physics 2023-11-08 Johanna Potyka , Kathrin Schulte

A semi-implicit Lax-Wendroff kinetic scheme is developed for hydrodynamic phonon transport in solid materials based on the Boltzmann transport equation under the double relaxation time approximation, in which both the normal and resistive…

Computational Physics · Physics 2026-01-30 Shijie Li , Hong Liang , Songze Chen , Chuang Zhang