FRAM—Nonlinear damping algorithms for the continuity equation

Abstract A nonlinear filtering methodology has been developed for the numerical solution of the convective terms in the Eulerian form of the hydrodynamic equations. FRAM (Filtering Remedy and Methodology) introduces a strong local nonlinear dissipation into each of the governing equations to dampen non-physical noise due to the properties of the solution algorithm selected for the convective terms in the equations. The technique is developed for the multidimensional continuity equation and tested on several differencing schemes in both one and two spatial dimensions. The technique is general in that there are no undetermined coefficients.