Numerical errors may be introduced in some numerical methods of solving differential equations because of their nature. Discretizing a continuum medium would result in changing the wave velocity and inducing numerical errors into the solution. Some methods using strong formulations are based on the Taylor expansion. Therefore, using only a finite number of Taylor series terms for particle simulations introduces truncation errors.
Truncation of the Taylor expansion is also the reason for developing two other types of error. The first, called dispersion error appears in the form of extra vibration in high frequency modes that can result in solution instability in some problems. Another type of error is dissipation and may cause decrease in wave amplitude.
Particle methods such as SPH [
] and CSPM [
], are also involved with truncation errors. A number of methods have already been proposed for removing dispersion from particle methods such as adding artificial stress. However these methods become energy dissipative resulting in wave amplitude decays after several time steps.
In this paper further investigation is performed to study the roots of dispersion and dissipation errors in particle methods. A new procedure is proposed for eliminating dispersion and stabilizing the solution, based on the CSPM particle method and the Newmark time integration scheme. The results are compared with other existing methods.