EXACT RESOLUTION ALGORITHMS FOR LINEAR GRID TRANSPORT (PREPRINT IBRAE-2001-08)

Preprint IBRAE-2001-08

Goloviznin V.M., Karabasov S.A.

A radically new numerical algorithm is presented that is free from traditional approximation viscosity and dispersion. The new algorithm called Jumping Transport Algorithm (JTA) allows one to calculate exactly the co-ordinates of strong discontinuities on a sub grid-cell scale. The algorithm is explicit, two-time-layer and operates with a fixed compact computational stencil.

JTA has a linearity property, i.e. the principle of linear superposition is valid for its solutions. For the linear advection equation the algorithm gives the exact solution in the sense of integral averages over computational cells. Under all time steps satisfying the condition mod (CFL)£1 the JTA can translate an initial grid-delta-function without distortion for unlimited distance.

An algorithm extension to the convection-diffusion equation is presented. Numerical examples are provided illustrating uncommon features of the algorithm.   

Bibliographical reference

Goloviznin V.M., Karabasov S.A. EXACT RESOLUTION ALGORITHMS FOR LINEAR GRID TRANSPORT (in Russian). Preprint IBRAE-2001-08. Moscow: Nuclear Safety Institute, May 2001. 41 p. — Refs.: 17 items.