An improved smoothed particle hydrodynamics approach using new inverse kernel function

Abstract

The main limitation of Smoothed Particle Hydrodynamics (SPH) method that resists the method's potential is its lack of providing stability and accuracy to the numerical technique. We improve the accuracy of the standard SPH technique, by formulating a new inverse logarithmic kernel function. This new kernel function is derived based on the underlying properties of kernel functions. The approximation technique used here is based on the Moving Least Squares based technique. The adequacy of the proposed kernel function is tested by simulation of 2D shock wave propagation and 3D dam-break free surface flow against a cuboidal obstacle. The method was validated against experimental data by Kleefsman et al., [1]. The numerical results reveal that our new SPH approach using inverse logarithmic kernel function outperforms existing ones in particle restoration, zero error, better accuracy and enhanced efficiency in kernel approximation. This new kernel function showed some improvement over existing kernels by showing very less error approximation value of 0.035h2. The results showed some improvements over standard technique by being capable of handling problems with large deformations accurately and precisely.

Keywords

• Inverse logarithmic function
• Moving least squares approximation
• Shock wave propagation
• 3D dam-break flow
• Zero error