粒子法による拡散方程式の決定論的一解法における精度と安定性

抄録

Numerical experiments have been performed to study accuracy and stability of a deterministic particle method for the diffusion equation. The diffusion velocity introduced in our method is defined as the velocity which is proportional to the density gradient and the diffusion coefficient ν, and inversely proportional to the density. The one-dimensional case is considered using the Gaussian distribution for the shape function, and the Forward-Euler scheme for solving the ordinary differential equations. The effect of the shape parameter σ, the time step Δt and the particle number on numerical erros is investigated. It is found that the stability depends not on the distance between the particles, but on the non-dimensional time step νΔt/σ², and that numerical errors of stable solutions are almost constant in spite of the variation of νΔt/σ². Criteria for obtaining the stable solutions and accurate density distribution are also given.