Analysis of the Heterogeneous Multiscale Method for Gas Dynamics
نویسندگان
چکیده
We carry out an error analysis for the heterogeneous multi-scale method for the case when the macroscale process is that of gas dynamics or more generally nonlinear conservation laws and the microscale process is an atomistic model such as kinetic Monte Carlo methods or molecular dynamics (MD). We will consider problems of type B as defined in [4], i.e. the macroscale constitutive relations are unknown and are extracted from the microscopic model. In addition to the standard error in the macroscale solver, a new error term occurs in estimating the data, here the fluxes. This new error term consists of three parts: the relaxation error, the sampling error and the error due to the finite size of the atomistic simulation. Our results serve as guidelines for designing multiscale methods, as was done in [13, 16].
منابع مشابه
Dynamics of Macro–Nano Mechanical Systems; Fixed Interfacial Multiscale Method
The continuum based approaches don’t provide the correct physics in atomic scales. On the other hand, the molecular based approaches are limited by the length and simulated process time. As an attractive alternative, this paper proposes the Fixed Interfacial Multiscale Method (FIMM) for computationally and mathematically efficient modeling of solid structures. The approach is applicable to mult...
متن کاملThe Heterogeneous Multiscale Method and the “Equation-free” Approach to Multiscale Modeling
In many problems of multiscale modeling, we are interested in capturing the macroscale behavior of the system with the help of some accurate microscale models, bypassing the need of using empirical macroscale models. This paper gives an overview of the recent efforts on establishing general strategies for designing such algorithms. After reviewing some important classical examples, the Car-Parr...
متن کاملVARIATIONAL HOMOTOPY PERTURBATION METHOD FOR SOLVING THE NONLINEAR GAS DYNAMICS EQUATION
A. Noor et al. [7] analyze a technique by combining the variational iteration method and the homotopy perturbation method which is called the variational homotopy perturbation method (VHPM) for solving higher dimensional initial boundary value problems. In this paper, we consider the VHPM to obtain exact solution to Gas Dynamics equation.
متن کاملAccelerated Simulation of a Heavy Particle in a Gas of Elastic Spheres
A new, accelerated algorithm for a system of elastic hard-spheres in which one of the particles (a colloid) is significantly heavier than the others is presented. The algorithm follows the framework of the stochastic heterogeneous multiscale method. It is shown that, in the limit in which the ratio between the light and the heavy particles approaches zero, the dynamics of the colloid is given b...
متن کاملA multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks
We present a multiscale model for numerical simulations of dynamics of crystalline solids. The method combines the continuum nonlinear elasto-dynamics model, which models the stress waves and physical loading conditions, and molecular dynamics model, which provides the nonlinear constitutive relation and resolves the atomic structures near local defects. The coupling of the two models is achiev...
متن کامل