Particle-grid methods for reacting flows in porous media with application to Fisher's equation

Abstract A two-step particle-in-cell model is developed for reactive mass transport problems in subsurface porous formations and applied to a model nonlinear diffusion-reaction system. Simulations progress by using a random walk particle method to diffuse or advect solute mass, represented here as a collection of particles, followed by a numerical integration step to determine changes in mass due to reaction processes on a grid. Techniques for mapping mass from the particles to the grid and vice versa are discussed. Numerical simulations of the so-called Fisher equation are compared to analytical solutions in the form of a steady travelling wave and a pertubed system undergoing a transition between two different steady waves. The approximations used in the approach are studied and discussed in terms of its future application to practical multidimensional, multicomponent transport problems.

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