# schems and algorithms

## SIMPLE scheme (1/3): Theory

as I learned from the awesome book Derivation of SIMPLE scheme for 1D uniform grid A steady momentum equation may be wrote as follows. If it is one dimensional, the momentum and continuity equations are as follows (2) and (3): Representing pressure and velocity on the cell centre may lead to so called checker board …

## High Resolution schemes

HR scheme = Higher Order Scheme + a Convection Boundedness Criterion HR scheme can be obtained by either of the following method Smoothening an unbounded Higher Order scheme with diffusive flux. Enhancing a first order upwind scheme with a limited anti-diffusive flux (TVD schemes). Two frameworks used for convection boundedness are Normalized Variable Formulation (NVF) …