Related papers: A class of new linear, efficient and high-order im…
For the incompressible Navier--Stokes system with variable density and viscosity, we propose and analyse an IMEX framework treating the convective and diffusive terms semi-implicitly. This extends to variable density and second order in…
Euler--Euler or volume-averaged Navier--Stokes equations are used in various applications to model systems with two or more interpenetrating phases. Each fluid obeys its own momentum and mass equations, and the phases are typically coupled…
In this work we study different Implicit-Explicit (IMEX) schemes for incompressible flow problems with variable viscosity. Unlike most previous work on IMEX schemes, which focuses on the convective part, we here focus on treating parts of…
We propose and study two second-order in time implicit-explicit (IMEX) methods for the coupled Stokes-Darcy system that governs flows in karst aquifers. The first is a combination of a second-order backward differentiation formula and the…
We construct high-order semi-discrete-in-time and fully discrete (with Fourier-Galerkin in space) schemes for the incompressible Navier-Stokes equations with periodic boundary conditions, and carry out corresponding error analysis. The…
Earth system models are composed of coupled components that separately model systems such as the global atmosphere, ocean, and land surface. While these components are well developed, coupling them in a single system can be a significant…
In this paper we construct new fully decoupled and high-order implicit-explicit (IMEX) schemes for the two-phase incompressible flows based on the new generalized scalar auxiliary variable approach with optimal energy approximation…
Consistent splitting schemes are among the most accurate pressure segregation methods, incurring no splitting errors or spurious boundary conditions. Nevertheless, their theoretical properties are not yet fully understood, especially when…
Coupled systems of free flow and porous media arise in a variety of technical and environmental applications. For laminar flow regimes, such systems are described by the Stokes equations in the free-flow region and Darcy's law in the porous…
We develop a numerical scheme for a two-phase immiscible flow in heterogeneous porous media using a structured grid finite element method, which have been successfully used for the computation of various physical applications involving…
Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to…
We construct and analyze first- and second-order implicit-explicit (IMEX) schemes based on the scalar auxiliary variable (SAV) approach for the magneto-hydrodynamic equations. These schemes are linear, only require solving a sequence of…
We propose a second-order implicit-explicit (IMEX) time-stepping scheme for the isentropic, compressible Cahn-Hilliard-Navier-Stokes equations in the low Mach number regime. The method is based on finite differences on staggered grids and…
Implicit-explicit (IMEX) time integration schemes are well suited for nonlinear structural dynamics because of their low computational cost and high accuracy. However, stability of IMEX schemes cannot be guaranteed for general nonlinear…
We derive a homogenized macroscopic model for fluid flows over ordered homogeneous porous surfaces. The unconfined free-flow is described by the Navier-Stokes equation, and the Darcy equation governs the seepage flow within the porous…
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…
A stable added-mass partitioned (AMP) algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and compressible elastic-solids. The AMP scheme remains stable and second-order accurate even…
This article aims at developing a high order pressure-based solver for the solution of the 3D compressible Navier-Stokes system at all Mach numbers. We propose a cell-centered discretization of the governing equations that splits the fluxes…
We consider the dynamics of two-phase fluids, in particular the moving contact line, on a solid substrate. The dynamics are governed by the sharp-interface model consisting of the incompressible Navier-Stokes\slash Stokes equations with the…
We consider a coupled model of free-flow and porous medium flow, governed by stationary Stokes and Darcy flow, respectively. The coupling between the two systems is enforced by introducing a single variable representing the normal flux…