A GPU-based compact conservative characteristic finite volume parallel algorithm for advection diffusion equations

Abstract

This study introduces a novel parallel algorithm for efficiently solving two-dimensional advection-diffusion problems with constant diffusion coefficient, specifically designed for implementation on GPU. The algorithm is compact, conservative, and inherently parallel, offering second-order accuracy in time and fourth-order accuracy in space. It employs a second-order operator splitting method to decompose the two-dimensional problem into one-dimensional subproblems, significantly enhancing parallelism in computations. The convective term is addressed using the characteristic method, which ensures high accuracy in time and allows for larger time steps. The conservative interpolation technique is implemented for integration within the Lagrangian tracking cell. For the diffusion term, we average along the characteristic curves and derive the discrete fluxes that are continuous at the cell boundaries. Taking advantage of the compact scheme, only three cells are required for the unknowns to achieve spatial fourth order accuracy. The primary computational tasks are performed on the GPU, distributing the computational load evenly across multiple cores. Numerical experiments demonstrate the conservation property and convergence rates of the new algorithm and its effectiveness in solving problems with steep fronts. The results also indicate the algorithm's superior computational speed compared to traditional CPU computations.