The influence of source terms on a gradient-based curvilinear grid scheme applied to a reacting flow

One-dimensional simulations provide an appropriate level of detail for studying the reactor dynamics of gas–solid metal hydride absorption heat pumps, which are a class of reacting flows. Because of the high energy densities and consequent difficulty in optimizing the reactors for finite time thermal performance, steep concentration gradients develop near energy transfer boundaries. With a uniform and fixed grid capable of resolving the gradients, the computational cost of a simulation can be considerable. Adaptive grid methods have been shown to reduce the computational cost in several classes of problems by reducing the overall discretization error compared to fixed grids using the same number of nodes through redistribution of node density. However the class of problems including mass and energy source terms, which are a prominent feature in reacting flows, are not well represented in the literature. In this paper an adaptive moving grid formulation is developed for a model of a metal hydride heat pump and the influence of the source terms evaluated. The grid satisfies an elliptic mesh equation to ensure smoothness, and grid motion is determined by a gradient-based logarithmic weight function of the absorbed hydrogen concentration, which avoids grid collapse. The strategy is shown to improve the resolution of monotonic gradients near heat transfer boundaries. The scheme performs less well when features exhibiting curvature appear simultaneously.