Related papers: Numerical Considerations for Advection-Diffusion P…
An improved numerical scheme is proposed for advection-dominated advection-diffusion problem. The scheme is based on Galerkin finite element method (FEM) with basis enriched with approximations to residual-free bubbles. The stabilisation…
In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large…
Numerical continuation techniques are powerful tools that have been extensively used to identify particular solutions of nonlinear dynamical systems and enable trajectory design in chaotic astrodynamics problems such as the Circular…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…
Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet,…
Regularized optimal mass transport (rOMT) problem adds a diffusion term to the continuity equation in the original dynamic formulation of the optimal mass transport (OMT) problem proposed by Benamou and Brenier. We show that the rOMT model…
The study of fluids has been a topic of intense research for several hundred years. Over the years, this has further increased due to improved computational facility, which makes it easy to numerically simulate the fluid dynamics, which was…
A low-Mach-number flow, in the laminar regime, has intrinsically two characteristic spatial scales for a given time scale, or two characteristic temporal scales for a given spatial scale, and these dual scales are very different due to the…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
We study the computation of coupled advection-diffusion-reaction equations by the Schwarz waveform relaxation method. The study starts with linear equations, and it analyzes the convergence of the computation with a Dirichlet condition, a…
We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite…
Linear stationary reaction-convection-diffusion equations with Dirichlet boundary conditions are approximated using a simple finite difference method corresponding to central differences and the addition of a high-order stabilization term…
We propose two closely--related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and…
When comparing measurements to numerical simulations of moisture transfer through porous materials a rush of the experimental moisture front is commonly observed in several works shown in the literature, with transient models that consider…
We consider numerical methods for linear parabolic equations in one spatial dimension having piecewise constant diffusion coefficients defined by a one parameter family of interface conditions at the discontinuity. We construct immersed…
A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary…
Several cardiovascular diseases are caused from localised abnormal blood flow such as in the case of stenosis or aneurysms. Prevailing theories propose that the development is caused by abnormal wall-shear stress in focused areas.…
We propose a novel method for the direct numerical simulation of interfacial flows involving large density contrasts, using a Volume-of-Fluid method. We employ the conservative formulation of the incompressible Navier-Stokes equations for…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
Recent advances have allowed to tackle exact path-space probabilistic representations of macroscopic advection-diffusion models involving advection nonlinearities by step forward approaches in terms of continuous branching stochastic…