Semi-Decoupled Second-Order Consistency Correction for Smoothed Particle Hydrodynamics

We present an approximate second-order consistent smoothed particle hydrodynamics method which uses the 1D solutions to approximate the 2D second order derivatives. The numerical tests of the analytic functions show that the method is exact for regular arrangements of interpolation points, while in the disordered areas the accuracy is lower than the exact solution of the second-order consistent modified smoothed particle hydrodynamics, but still better that the standard version or the so-called decoupled finite particle method. We applied the new model to the flow of a fluid around a circular solid obstacle and found that the use of a corrected semi-decoupled second-order consistent SPH gives better accuracy for lower resolutions allowing for a more efficient numerical model and also easier to extend to 3D