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A FINITE-VOLUME PARTICLE METHOD FOR COMPRESSIBLE FLOWS

Dietmar Hietel, Konrad Steiner, Jens Struckmeier

Open publisher page 86 citations

Abstract

We derive a new class of particle methods for conservation laws, which are based on numerical flux functions to model the interactions between moving particles. The derivation is similar to that of classical finite-volume methods; except that the fixed spatial mesh in a finite-volume method is substituted by so-called mass packets of particles. We give some numerical results on a shock wave solution for Burgers equation as well as the well-known one-dimensional shock tube problem.

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What this paper is about

We derive a new class of particle methods for conservation laws, which are based on numerical flux functions to model the interactions between moving particles. The derivation is similar to that of classical finite-volume methods; except that the fixed spatial mesh in a finite-volume method is substituted by so-called mass packets of particles. We give some numerical results on a shock wave solution for Burgers equation as well as the well-known one-dimensional shock tube problem.

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OpenAlex reports 86 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We derive a new class of particle methods for conservation laws, which are based on numerical flux functions to model the interactions between moving particles. The derivation is similar to that of classical finite-volume methods; except that the fixed spatial mesh in a finite-volume method is substituted by so-called mass packets of particles. We give some numerical results on a shock wave solution for Burgers equation as well as the well-known one-dimensional shock tube problem.

Key concepts: Finite volume method, Conservation law, Shock wave, Compressibility, Particle (ecology), Conservation of mass, Compressible flow, Mathematics

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