Enhancing Computational Precision for Lattice Boltzmann Schemes in Porous Media Flows

Abstract: We reassess a method for increasing the computational accuracy of lattice Boltzmann schemes by a simple transformation of the distribution function originally proposed by Skordos which was found to give a marginal increase in accuracy in the original paper. We restate the method and give further important implementation considerations which were missed in the original work and show that this method can in fact enhance the precision of velocity field calculations by orders of magnitude and does not lose accuracy when velocities are small, unlike the usual LB approach. The analysis is framed within the multiple-relaxation-time method for porous media flows, however the approach extends directly to other lattice Boltzmann schemes. First, we compute the flow between parallel plates and compare the error from the analytical profile for the traditional approach and the transformed scheme using single (4-byte) and double (8-byte) precision. Then we compute the flow inside a complex-structured porous medium and show that the traditional approach using single precision leads to large, systematic errors compared to double precision, whereas the transformed approach avoids this issue whilst maintaining all the computational efficiency benefits of using single precision.