Accuracy and dispersion of difference schemes

Numerical simulation of shock-wave processes in elastic media and structures. Part I: Solving method and algorithms

“…The requirement of convergence of the domains of dependence (CDD) is formulated below as a condition allowing ND minimization. Note that the NDM principle was originally formulated as a requirement of coincidence of the solutions of dispersion equations of the continual and discrete models in [9] and in subsequent papers [10][11][12][13][15][16][17][18][19][20][21][22][23], where numerical simulation of various non-stationary problems (including geodynamic ones) was performed using NDM. In linear one-dimensional problems, NDM and CDD principles are equivalent, as shown below.…”

“…Spatial problems of special kinds were an exception. Thus, in problems of layered media fracture [13,14], the interaction of waves of different types was postulated in local lines, while in the rest of the region the waves were separated. In [15-17, 21, 22], the expansion in Fourier series along the circumferential coordinate was applied, and the problem was reduced to the solution of a system of one-dimensional non-interconnected wave equations for each harmonic (excluding numerical dispersion).…”