A Piecewise Uniform Adaptive Grid Algorithm for Nonlinear Dispersive Wave Equations

A geometrically based grid refinement technique for multiphase flows

“…In the original implementation (Fraga and Morris, 1996), it was noted that it was not necessary to use the solution values alone to identify regions of uniformity. Instead, an approximation to the first derivative of the solution profile, using a simple first-order finite difference approximation, could be used to locate regions of large change in the spatial dimension, such as shocks.…”

“…Extension of PAG algorithm (Fraga and Morris, 1996) for adaptive grid generation with multiple dependent variables Given: Profile for each of m indicator variables I i at positions x i , i = 1, . .…”

“…As an alternative, a piecewise-uniform adaptive grid (PAG) method was developed by Fraga and Morris (1996). This technique, originally developed for the capture of soliton waves in dispersive equations, employs a single, piecewise uniform grid in which the spatial discretisation and time stepping algorithm are wholly decoupled.…”

Efficient simulation of chromatographic separation processes

“…Once the new mesh has been developed, a question arises as to the means of transferring the solution from the old grid to the new one. Fraga and Morris (1996) suggested the use of quadratic or cubic interpolation over a simpler linear interpolation; they showed that the latter would increase the dissipation of the solution. However, only the linear interpolation has practically been found to be effective in the case of shocks (Fraga, 1998;Brown et al, 2014) due to oscillations introduced during the reconstruction phase when using higher order interpolations.…”

“…While not requiring such complex data structures as the former, the moving grid technique has the drawback of requiring the solution of additional equations. The Piecewise Uniform Adaptive Grid (PAG) method (Fraga and Morris, 1996;Brown et al, 2015a), originally developed for the capture of soliton waves in dispersive wave equations, benefits from a relatively simple structure. It employs a single, piecewise uniform grid in which the spatial discretisation and time stepping algorithm are wholly decoupled and the opportunity to apply various solvers for the temporal evolution of the problem exists.…”