Higher order approximation methods for the Boltzmann equation
type: Item
instance of: scholarly article
title: Higher order approximation methods for the Boltzmann equation
zbMATH Open document ID: 0905.65134
author: Taku Ohwada
published in: Journal of Computational Physics
publication date: 1999-01-05T00:00:00Z
review text: The paper deals with a higher-order time difference method for the spatially nonhomogeneous Boltzmann equation \[ \begin{multlined} {\partial f\over \partial t}(X,\xi,t) +\xi \cdot {\partial f\over \partial X} (X,\xi,t) =Q\bigl(f(X, \xi,t), f(X,\xi,t) \bigr) [\xi],\\ 0<t\leq \Delta t, \quad f(X,\xi,0) =f_0(X,\xi). \end{multlined} \] The proposed method consists of two steps, as the first one is the same as the convection step in the splitting method while the second one takes into account not only the collision term but also its variation along the characteristic line.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 1140518
zbMATH Keywords: finite difference method
zbMATH Keywords: higher-order accuracy
zbMATH Keywords: time difference method
zbMATH Keywords: Boltzmann equation
zbMATH Keywords: splitting method
reviewed by: Emil Minchev
MaRDI profile type: Publication
full work available at URL: jcph.1997.5869
OpenAlex ID: W2049493974
cites work: Direct simulation of gas flows at the molecular level
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cites work: Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard-sphere molecules
cites work: The inclusion of collisional effects in the splitting scheme
cites work: On the Construction and Comparison of Difference Schemes
DOI: 10.1006/JCPH.1997.5869
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description: scientific article; zbMATH DE number 1140518