Related papers: Numerical strategy on the grid orientation effect …
We address a numerical instability that arises in the directionally split computation of hydrodynamic flows when shock fronts are parallel to a grid plane. Transverse oscillations in pressure, density and temperature are produced that are…
Context. High-resolution numerical methods have been developed for nonlinear, discontinuous problems as they appear in simulations of astrophysical objects. One of the strategies applied is the concept of artificial viscosity. Aims.…
The paper develops a method for the numerical simulation of a free-surface flow of incompressible viscous fluid around a streamlined body. The body is a rigid stationary construction partially submerged in the fluid. The application we are…
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear…
This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on problems with discontinuous initial porosities. A convergent…
Numerical simulation of viscoelastic flows is challenging because of the hyperbolic nature of viscoelastic constitutive equations. Despite their superior accuracy and efficiency, pseudo-spectral methods require the introduction of…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…
In this paper we consider the numerical approximation of the two-phase membrane (obstacle) problem by finite difference method. First, we introduce the notion of viscosity solution for the problem and construct certain discrete nonlinear…
Parasitic currents still pose a significant challenge for the investigation of two-phase flow in Lab-on-Chip (LoC) applications with Volume-of-Fluid (VoF) simulations. To counter the impact of such spurious velocity fields in the vicinity…
Fluid discontinuities, such as shock fronts and vortex sheets, can reflect waves and become unstable to corrugation. Analytical calculations of these phenomena are tractable in the simplest cases only, while their numerical simulations are…
A numerical analysis of the effect of artificial viscosity is undertaken in order to understand the effect of numerical diffusion on numerical boundary feedback control. The analysis is undertaken on the linear hyperbolic systems…
This paper presents a new boundary integral equation (BIE) method for simulating particulate and multiphase flows through periodic channels of arbitrary smooth shape in two dimensions. The authors consider a particular system---multiple…
A defect-deferred correction method, increasing both temporal and spatial accuracy, for fluid-fluid interaction problem with nonlinear interface condition is considered by geometric averaging of the previous two-time levels. In the defect…
Geometrical optics (GO) is often used to model wave propagation in weakly inhomogeneous media and quantum-particle motion in the semiclassical limit. However, GO predicts spurious singularities of the wavefield near reflection points and,…
The general pressure equation (GPE) is a new method proposed recently by Toutant (J. Comput. Phys., 374:822-842 (2018)) for incompressible flow simulation. It circumvents the Poisson equation for the pressure and performs better than the…
We investigate two common numerical techniques for integrating reversible moist processes in atmospheric flows in the context of solving the fully compressible Euler equations. The first is a one-step, coupled technique based on using…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…