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The support operator method designs mimetic finite difference schemes by first constructing a discrete divergence operator based on the divergence theorem, and then defining the discrete gradient operator as the adjoint operator of the divergence based on the Gauss theorem connecting the divergence and gradient operators, which remains valid also in the… (More)

A new optimization-based synchronized flux-corrected conservative interpolation (remap-ping) of mass and momentum for arbitrary Lagrangian–Eulerian hydro methods is described. Fluxes of conserved variables – mass and momentum – are limited in a synchronous way to preserve local bounds of primitive variables – density and velocity. In numerical simulations… (More)

The article deals with automation of the process of numerical solving of partial differential equations systems (PDES) by means of computer algebra. For solving PDES the finite difference method is applied. The computer algebra system REDUCE and the numerical programming language FORTRAN are used in the methodology presented, its main aim being to speed up… (More)

The paper deals with the formalization of the basic operator method for construction of difference schemes for the numerical solving of partial differential eq~ua-tions. The strength of the basic operator method lies on the fact that it produces fully conservative difference schemes. The difference mesh can be non-orthogonal but has to be logically… (More)

- Richard Liska
- 2001

The majority of large-scale scientific computation problems fall into the area of numerical simulations of real world systems. Such systems are usually described by a mathematical model in the form of a system of partial differential equations (PDEs) which are solvable only numerically. The productivity of particular numerical PDEs solver development can be… (More)