Related papers: An implicit-explicit solver for a two-fluid single…
In the present paper we propose a reduced temperature non-equilibrium model for simulating multicomponent flows with inter-phase heat transfer, diffusion processes (including the viscosity and the heat conduction) and external energy…
We introduce a coupled Cahn-Hilliard Navier-Stokes model that governs the two-phase dynamics of a system that consists of a fluid and a solid phase and prove its thermodynamic consistency. Moreover, we present an associated fully-discrete…
We consider two implicit approximation schemes of the one-dimensional supercooled Stefan problem and prove their convergence, even in the presence of finite time blow-ups. All proofs are based on a probabilistic reformulation recently…
We propose a second-order implicit-explicit (IMEX) time-stepping scheme for the isentropic, compressible Cahn-Hilliard-Navier-Stokes equations discretized on staggered (MAC) grids. The scheme is based on finite difference approximations…
High-order adaptive time-stepping algorithms are of significant practical value and theoretical interest for accelerating long-time fluid-flow simulations and resolving complex dynamical behaviors. While several high-order implicit-explicit…
We show that the one-dimensional (1D) two-fluid model (TFM) for stratified flow in channels and pipes (in its incompressible, isothermal form) satisfies an energy conservation equation, which arises naturally from the mass and momentum…
An implicit Euler finite-volume scheme for an $n$-species population cross-diffusion system of Shigesada--Kawasaki--Teramoto-type in a bounded domain with no-flux boundary conditions is proposed and analyzed. The scheme preserves the formal…
In this paper a new hybrid semi-implicit finite volume / finite element (FV/FE) scheme is presented for the numerical solution of the compressible Euler and Navier-Stokes equations at all Mach numbers on unstructured staggered meshes in two…
We consider high order, implicit Runge-Kutta schemes to solve time-dependent stiff PDEs on dynamically adapted grids generated by multiresolution analysis for unsteady problems disclosing localized fronts. The multiresolution finite volume…
We propose a new curl-free and thermodynamically compatible finite volume scheme on Voronoi grids to solve compressible heat conducting flows written in first-order hyperbolic form. The approach is based on the definition of compatible…
In this paper we design, analyze and simulate a finite volume scheme for a cross-diffusion system which models chemotaxis with local sensing. This system has the same Lyapunov function (or entropy) as the celebrated minimal Keller-Segel…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
The paper focuses on the development of numerical methods for the compressible Euler equations. It is well-known that if the Mach number is small, the system becomes stiff and hence explicit schemes suffer from severe time-step…
An asymptotic preserving and energy stable scheme for the Euler-Poisson system under the quasineutral scaling is designed and analysed. Correction terms are introduced in the convective fluxes and the electrostatic potential, which lead to…
In this paper we propose an efficient second order well balanced finite volume method for modeling complex free surface flows at the aid of a simple diffuse interface method. The employed physical model is a two-phase model derived from the…
The goal of this paper is to develop 2nd order Implicit-Explicit Runge-Kutta (IMEX-RK) finite volume (FV) schemes for solving 1d parabolic PDEs for option pricing, with possible nonlinearities in the source and advection terms. The spatial…
The Navier-Stokes-Korteweg (NSK) equations are a classical diffuse-interface model for compressible two-phase flow. As direct numerical simulations based on the NSK system are quite expensive and in some cases even impossible, we consider a…
We study a time implicit Finite Volume scheme for degenerate Cahn-Hilliard model proposed in [W. E and P. Palffy-Muhoray. Phys. Rev. E, 55:R3844-R3846, 1997] and studied mathematically by the authors in [C. Canc\`es, D. Matthes, and F.…
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…
This paper presents a finite volume method for simulating two-phase flows using a level set approach coupled with volume of fluid method capable of simulating sharp fluid interfaces. The efficiency of the method is a result of the fact that…