Related papers: Convecting reference frames and invariant numerica…
In large-eddy simulations (LES) a computational-domain translation velocity can be used to improve performance by allowing longer time-step intervals. The continuous equations are Galilean invariant, however, standard…
In this paper, we prove the convergence of a class of finite volume schemes for the model of coupling between a Burgers fluid and a pointwise particle introduced in [LST08]. In this model, the particle is seen as a moving interface through…
We study the discretization, convergence, and numerical implementation of recent reformulations of the quadratic porous medium equation (multidimensional and anisotropic) and Burgers' equation (one-dimensional, with optional viscosity), as…
For the one dimensional Burgers equation with a random and periodic forcing, it is well-known that there exists a family of invariant measures, each corresponding to a different average velocity. In this paper, we consider the coupled…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…
Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions. While originally designed for constructing invariant finite difference schemes, we extend the usage of…
This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits both nonlocal and nonlinear behaviour making the numerical…
We present and analyze in a unified setting two schemes for the numerical discretization of a Darcy-Forchheimer fluid flow model coupled with an advection-diffusion equation modeling the temperature distribution in the fluid. The first…
Inverse problems of partial differential equations are ubiquitous across various scientific disciplines and can be formulated as statistical inference problems using Bayes' theorem. To address large-scale problems, it is crucial to develop…
I analyse a generalised Burger's equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the finite difference model accurately models the…
We consider a discretization of Caputo derivatives resulted from deconvolving a scheme for the corresponding Volterra integral. Properties of this discretization, including signs of the coefficients, comparison principles, and stability of…
We study experimentally the impact of inertial reference frame changes on overdamped Brownian motion. The reference frame changes are implemented by inducing, with a laser, laminar convection flows in a column of fluid where Brownian…
We present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare the standard Galerkin discretization using the linear…
In this study we have developed a flexible and efficient numerical scheme for the simulation of three-dimensional incompressible flows in spherical coordinates. The main idea, inspired by a similar strategy as (Verzicco, R., Orlandi, P.,…
We use a generic framework, namely the gradient discretisation method (GDM), to propose a unified numerical analysis for general time-dependent convection-diffusion-reaction models. We establish novel results for convergence rates 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,…
In this work we study the stability, convergence, and pressure-robustness of discretization methods for incompressible flows with hybrid velocity and pressure. Specifically, focusing on the Stokes problem, we identify a set of assumptions…
In this article we study generalizations of the inhomogeneous Burgers equation. First at the operator level, in the sense that we replace classical differential derivations by operators with certain properties, and then we increase the…
When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the…