Abstract
We present a new method for solving two-dimensional convection-dominated convection-diffusion equations containing spatially and temporally localized source terms. The method uses grid-free transport: particles which carry point values of the concentration gradient move by convection and undergo random-walk to simulate diffusion. No numerical diffusion is introduced. Equations for the evolution of the gradient values are solved. The concentration is recovered from the particle data by solving Poisson equations. The method is applied to problems in rotational and elongational flow fields. Numerical results demonstrating convergence of the method are presented.
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