Optimization of the Parameters of Smoothed Particle Hydrodynamics Method, Using Evolutionary Algorithms

Smooth particle hydrodynamics (SPH) is a mesh free numerical method for solving hydrodynamical equations. For its functioning, the method uses; one integer-domain parameter (the total number of particles) and three real domain parameters (smoothing parameters and artificial viscosity). For a given problem (geometry and initial conditions) these parameters can be tuned to reduce the computational cost and improve the accuracy of the solutions. Optimized values of the SPH parameters using the evolutionary algorithms, Differential Evolution (DE) and Boltzmann Univariate Marginal Distribution Algorithm (BUMDA) are obtained for different Sod shock tube test problems. Comparison of the numerical solution of the physical variables with that of the exact solution shows that this optimization strategy can be used to make an initial guess of the SPH parameters based on the initial conditions of the simulation domain. The performance of the two algorithms are statistically compared.