Related papers: Implicit like time discretization for the one-phas…
With the Lattice Boltzmann method (using the BGK approximation) we investigate the dynamics of Hele-Shaw flow under conditions corresponding to various experimental systems. We discuss the onset of the instability (dispersion relation), the…
The dynamics of the interface between two immiscible fluids in a rotating Hele-Shaw cell are studied experimentally, theoretically and by phase-field simulations of the H-S equations. As the central, denser fluid is centrifuged, it forms…
The numerical modelling of convection dominated high density ratio two-phase flow poses several challenges, amongst which is resolving the relatively thin shear layer at the interface. To this end we propose a sharp discretisation of the…
Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial…
Some effects of surface tension on fully-nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are…
In this paper, we propose a tensor type of discretization and optimization process for solving high dimensional partial differential equations. First, we design the tensor type of trial function for the high dimensional partial differential…
We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed…
We present a second-order-in-time finite difference scheme for the Cahn-Hilliard-Hele-Shaw equations. This numerical method is uniquely solvable and unconditionally energy stable. At each time step, this scheme leads to a system of…
The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the…
Different formulations of interfacial force have been adopted in phase-field-based lattice Boltzmann method for two-phase flows. Although they are identical mathematically, their numerical performances may be different due to truncation…
We consider the efficient solution of strongly elliptic partial differential equations with random load based on the finite element method. The solution's two-point correlation can efficiently be approximated by means of an…
We consider the phase separation of binary fluids in contact with a surface which is preferentially wetted by one of the components of the mixture. We review the results available for this problem and present new numerical results obtained…
Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…
This work uses a linear relaxation method to develop efficient numerical schemes for the time-fractional Allen-Cahn and Cahn-Hilliard equations. The L1+-CN formula is used to discretize the fractional derivative, and an auxiliary variable…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
Using an integrable discrete Dirac operator, we construct a discrete version of the Weierstrass representation of time-like surfaces parametrized along isotropic directions in $R^{2,1}$, $R^{3,1}$ and $R^{2,2}$. The corresponding discrete…
In this paper, we develop a high order numerical method for the numerical solutions of scattering problems with slightly perturbed periodic surfaces in two dimensional spaces. Based on the regularity property introduced in Part I, the…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…
Saturation overshoot and pressure overshoot are studied by incorporating dynamic capillary pressure, capillary pressure hysteresis and hysteretic dynamic coefficient with a traditional fractional flow equation in one dimension. Using the…
In this work, we study the parallel-in-time iterative solution of coupled flow and geomechanics in porous media, modelled by a two-field formulation of the Biot's equations. In particular, we propose a new version of the fixed stress…