Model-Adaptive Simulation of Hyperbolic Moment Equations in One Dimension

The need for space- and time-adaptivity in rarefied gas simulations arises because different time-variable subdomains within a rarefied gas domain often require varying levels of modelling complexity. Different-order moment models are effective at describing rarefied gas flows with respective levels of complexity in each subdomain. In this work, a numerical method for the model-adaptive simulation of the non-linear Hyperbolic Moment Equations (HME) model is proposed to simulate a rarefied gas flow using an HME model with time- and space-dependent model order. The first step of the adaptive procedure is a domain decomposition into subdomains each modelled by an HME model of an appropriate order, using domain decomposition criteria that are based on the exact model difference between a higher-order HME model and a lower-order HME model and on chosen error thresholds. In the second step of the adaptive procedure, a non-linear adaptation of a recently developed padded buffer cell approach is presented to couple these varying-order HME models using a single finite volume scheme. Finally, a smoothing of the domain decomposition is proposed to limit oscillations generated by the coupling. While its performance depends on the thresholds and the smoothing parameter, the proposed model-adaptive simulation method yields accurate results while obtaining computational speedups of up to 40 percent compared to using a high-order HME model in the entire domain.