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Kinetic Meshless Method

Chandrashekar, Praveen and Deshpande, SM (2003) Kinetic Meshless Method. 2003-FM-10.

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Abstract

We propose a new method called the Kinetic Meshless Method (KMM), for the solution of time-dependent conservation laws that can be derived from a Boltzmann-type equation by taking suitable moments. An important characteristic of this method is its grid-free nature; it is able to use any type of grid or combination of grids, or even some distribution of nodes. All that the method requires is the specification of the connectivity, which consists of a cloud of neighbouring points around each point. For hyperbolic conservation laws, the method is stabilized by introducing an upwind-bias using the kinetic representation. A numerical order of accuracy of two is shown for a scalar conservation law even though the formal order of the method is one. Numerical second order accuracy is obained even on a highly non-uniform grid. We have applied the above method for the solution of the Euler equations by using the Maxwell-Boltzmann distribution function. In this case, it has been previously called KRIME, Kinetic Rotationally Invariant Method for Euler equations. We present a number of results on point distributions obtained from unstructured grids. Results are obtained on adapted grids and demonstrate the ability of the method to capture discontinuities sharply.

Item Type: Departmental Technical Report
Keywords: Conservation laws;Euler equations;kinetic method;meshless approximation;upwind scheme
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Division of Mechanical Sciences > Aerospace Engineering (Formerly, Aeronautical Engineering)
Date Deposited: 04 Jun 2004
Last Modified: 19 Sep 2010 04:12
URI: http://eprints.iisc.ernet.in/id/eprint/157

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