In the standard SPH method, the interaction between two particles might benot pairwise when the support domain varies, which can result in a reduction ofaccuracy. To deal with this problem, a modified SPH approach is presented inthis paper. First of all, a Lagrangian kernel is introduced to eliminatespurious distortions of the domain of material stability, and the gradient iscorrected by a linear transformation so that linear completeness is satisfied.Then, concepts of support and dual-support are defined to deal with theunbalanced interactions between the particles with different support domains.Several benchmark problems in one, two and three dimensions are tested toverify the accuracy of the modified SPH model and highlight its advantages overthe standard SPH method through comparisons.
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