Related papers: A new numerical strategy with space-time adaptivit…
In this paper we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual…
We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…
We use numerical simulations to study the dynamics of surface discharges, which are common in high-voltage engineering. We simulate positive streamer discharges that propagate towards a dielectric surface, attach to it, and then propagate…
In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with appropriate predictor-corrector method to achieve higher resolution. The underlying finite…
Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order $\alpha\in(0,1)$ in time, due to their many successful applications in engineering, physics, biology…
With the aim of efficiently simulating three-dimensional multiphase turbulent flows with a phase-field method, we propose a new discretization scheme for the biharmonic term (the 4th-order derivative term) of the Cahn-Hilliard equation.…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two main steps. In the first step, the space variable is…
A new solver featuring time-space adaptation and error control has been recently introduced to tackle the numerical solution of stiff reaction-diffusion systems. Based on operator splitting, finite volume adaptive multiresolution and high…
It is a challenge to numerically solve nonlinear partial differential equations whose solution involves discontinuity. In the context of numerical simulators for multi-phase flow in porous media, there exists a long-standing issue known as…
In this paper we present a novel algorithm for simulating geometrical flows, and in particular the Willmore flow, with conservation of volume and area. The idea is to adapt the class of diffusion-redistanciation algorithms to the Willmore…
Accurate and efficient numerical simulation of unconventional reservoirs is challenging. Long periods of transient flow and steep potential gradients occur due to the extreme conductivity contrast between matrix and fracture. Detailed…
Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…
Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
Modeling and simulation of High Power Microwave (HPM) breakdown, a multiscale phenomenon, is computationally expensive and requires solving Maxwell's equations (EM solver) coupled with a plasma continuity equation (plasma solver). In this…
To achieve efficient and accurate long-time integration, we propose a fast, accurate, and stable high-order numerical method for solving fractional-in-space reaction-diffusion equations. The proposed method is explicit in nature and…
We present a novel parametric finite element approach for simulating the surface diffusion of curves and surfaces. Our core strategy incorporates a predictor-corrector time-stepping method, which enhances the classical first-order temporal…
Kinetic instabilities are one of the most challenging aspects in computational plasma physics. Accurately capturing their onset and evolution requires fine resolution of the high-dimensional distribution functions of each relevant species,…
There are many interesting physical processes which involve the generation of high density plasmas in large volumes. However, when modeling these systems numerically, the large densities and volumes present a significant computational…