Abstract
Motivated by recent research on the iterative approach proposed for the smoothed particle hydrodynamics (ISPH) method, some ideas to improve the process are introduced. The standard procedure is enhanced iterating on the residuals preserving the matrix-free nature of the process. The method is appealing providing reasonable results with disordered data distribution too and no kernel variations are needed in the approximation. This work moves forward with a novel formulation requiring a lower number of iterations to reach a desired accuracy. The computational procedure is described and some results are introduced to appreciate the proposed formulation.
Highlights
Smoothed Particle Hydrodynamics is a popular kernel based approach introduced in astrophysics [4,5,6,7,8,9] and it is being increasingly used [3,10,11,12,13,14]
In [15] the standard procedure has been improved by means of an iterative approach refining the residuals
The iterative procedure adopted via residual iterations gives interesting results into
Summary
Mesh-free methods are promising approaches emerging in recent years as valid computational alternatives to grid-based ones. An approximant is generated by employing strictly definite positive kernel functions and the method, in convergence, improves the results without requiring evenly spaced data distribution. If the linear approximation order is ensured [16,17], the iterative procedure performs better. In a recent paper [18] some results on this improved approach have been presented, the algorithm can become prohibitive for the number of iterations. In this work, starting with the linear approximation order, a formulation which guarantees accuracy with a lower number of iterations is proposed and discussed.
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