Enhancing SPH using moving least-squares and radial basis functions
This work addresses accuracy limitations in SPH for computational fluid dynamics practitioners, offering a principled alternative to ad hoc smoothing-length selection.
The paper enhances smoothed particle hydrodynamics (SPH) by integrating moving least-squares (MLS) and radial basis functions (RBF) to improve particle approximation accuracy, deriving variationally-consistent hydrodynamic equations. The new method is demonstrated on the Sod shock tube problem, showing improved performance.
In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions constructed using: moving least-squares approximation (MLS); radial basis functions (RBF). Using MLS approximation is appealing because polynomial consistency of the particle approximation can be enforced. RBFs further appeal as they allow one to dispense with the smoothing-length -- the parameter in the SPH method which governs the number of particles within the support of the shape function. Currently, only ad hoc methods for choosing the smoothing-length exist. We ensure that any enhancement retains the conservative and meshfree nature of SPH. In doing so, we derive a new set of variationally-consistent hydrodynamic equations. Finally, we demonstrate the performance of the new equations on the Sod shock tube problem.