The dissolution of solids has created spectacular geomorphologies ranging from centimeter-scale cave scallops to the kilometer-scale “stone forests” China and Madagascar. Mathematically, processes are modeled by a Stefan problem, which describes how motion phase-separating interface depends on local concentration gradients, coupled fluid flow. Simulating these problems is challenging, requiring...

This article investigates the nonlinear, steady boundary layer flow and heat transfer of an incompressible Eyring-Powell non-Newtonian fluid from an isothermal sphere with Biot number effects. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The influ...

A boundary integral operator method for stochastic ray tracing in billiards was recently proposed in [1]. In particular, a phase-space boundary integral model for propagating uncertain ray or particle flows was described and shown to interpolate between deterministic and random models of the flow propagation. In this work we describe discretisation schemes for this class of boundary integral op...

Abstract. In this article, we consider the linearized inviscid shallow water equations in space dimension two in a rectangular domain. We implement a finite volume discretization and prove the numerical stability and convergence of the scheme for three cases that depend on the background flow ũ0, ṽ0, and φ̃0 (subor super-critical flow at each part of the boundary). The three cases that we consid...

In this paper we study the acoustic properties of a microstructured material such as glass wool or foam. In our model, the solid matrix is governed by linear elasticity and the surrounding fluid obeys Stokes equations. The microstructure is assumed to be periodic at some small scale ε and the viscosity coefficient of the fluid is assumed to be of order ε. We consider the time-harmonic regime fo...

‎in the present analysis‎, ‎we study the boundary layer flow of an incompressible viscous fluid near the two-dimensional stagnation-point flow over a stretching surface‎. ‎the effects of variable thickness and radiation are also taken into account and assumed that the sheet is non-flat‎. ‎using suitable transformations‎, ‎the governing partial differential equations are first converted to ordin...

The aim of the present paper is the development of an efficient numerical algorithm for the solution of magnetohydrodynamics flow problems for regular and irregular geometries subject to Dirichlet, Neumann and Robin boundary conditions. Toward this, the meshless point collocation method (MPCM) is used for MHD flow problems in channels with fully insulating or partially insulating and partially ...

We construct a solution to inverse mean curvature flow on an asymptotically hyperbolic 3-manifold which does not have the convergence properties needed in order to prove a Penrose–type inequality. This contrasts sharply with the asymptotically flat case. The main idea consists in combining inverse mean curvature flow with work done by Shi–Tam regarding boundary behavior of compact manifolds. As...

A volume penalization approach to simulate magnetohydrodynamic (MHD) flows in confined domains is presented. Here the incompressible visco-resistive MHD equations are solved using parallel pseudo-spectral solvers in Cartesian geometries. The volume penalization technique is an immersed boundary method which is characterized by a high flexibility for the geometry of the considered flow. In the p...