相关论文: Eikonal boundary condition for level set method

Given only a collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to solve elliptic partial differential equations (PDEs) supplemented with boundary conditions. Notice…

We study the initial boundary value problem for a heat equation in a domain containing a thin layer. The thermal conductivity of the layer is drastically different from that of the bulk of the domain; moreover, the layer is anisotropic and…

We consider the homogenization of the Navier-Stokes equation, set in a channel with a rough boundary, of small amplitude and wavelength $\epsilon$. It was shown recently that, for any non-degenerate roughness pattern, and for any reasonable…

We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. The new boundary procedure is applied to nonlinear IBVPs in…

In this paper, the solutions of Navier-Stokes equations with Dirichlet boundary conditions governing 2-D incompressible fluid flows are considered. A condition for boundary layer separation, which is determined by initial values and…

We present a new method for the numerical implementation of generating boundary conditions for a one dimensional Boussinesq system. This method is based on a reformulation of the equations and a resolution of the dispersive boundary layer…

Building upon recent results obtained in [7,8,9], we describe an efficient second order, A-stable scheme for solving the wave equation, based on the method of lines transpose (MOL$^T$), and the resulting semi-discrete (i.e. continuous in…

The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditions must be defined on a finite volume region outside the…

The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of…

The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper we…

We develop a model for steady, laminar boundary layers over small-scale textured surfaces. Although the texture is small relative to the boundary-layer thickness, it modifies the flow via a slip length. We use matched asymptotic expansions…

We consider the free boundary problem for the incompressible elastodynamics equations. At the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary and the pressure…

We introduce a non-reflecting boundary condition for the simulation of thermal flows with the lattice Boltzmann Method (LBM). We base the derivation on the locally one-dimensional inviscid analysis, and define target macroscopic values at…

Consider the Laplacian in a bounded domain in R^d with general (mixed) homogeneous boundary conditions. We prove that its eigenfunctions are `quasi-orthogonal' on the boundary with respect to a certain norm. Boundary orthogonality is proved…

In this paper, we deal with the initial value problem for a class of fully nonlinear parabolic equations with a singular Dirichlet boundary condition in one space dimension. The interior equation includes, for example, a fully nonlinear…

We present an explicit finite difference method to simulate the non-ideal multi-phase fluid flow. The local density and the momentum transport are modeled by the Navier-Stokes (N-S) equations and the pressure is computed by the Van der…

This paper is devoted to the theoretical and numerical investigation of the initial boundary value problem for a system of equations used for the description of waves in coastal areas, namely, the Boussinesq-Abbott system in the presence of…

A robust numerical methodology to predict equilibrium interfaces over arbitrary solid surfaces is developed. The kernel of the proposed method is the distance regularized level set equations (DRLSE) with techniques to incorporate the…

In this paper, we investigate a sixth order elliptic equation with the simply supported boundary conditions in a polygonal domain. We propose a new method that decouples the sixth order problem into a system of second order equations.…

This paper presents a new monolithic free-surface formulation that exhibits correct kinetic and potential energy behavior. We focus in particular on the temporal energy behavior of two-fluids flow with varying densities. Correct energy…