F. Liu et al., AN ADAPTIVE-GRID METHOD AND ITS APPLICATION TO STEADY EULER FLOW CALCULATIONS, SIAM journal on scientific computing (Print), 20(3), 1999, pp. 811-825
An adaptive remeshing procedure based on a cell volume deformation met
hod is presented. Starting with an initial grid, this method offers di
rect cell volume control through the specification of the transformati
on Jacobian. Grid points are moved with appropriate grid velocities so
that the specified cell volume distribution can be achieved at the en
d of the grid movement without adding or removing grid points. The gri
d velocities are determined by solving a scalar Poisson equation. This
method is applied to solving the compressible Euler equations. Comput
ational test cases of transonic flow over an airfoil are presented and
demonstrate the desired control of grid sizes across shock waves.