hp-Adaptive spectral element solver for reactor modeling

The study, analysis and optimization of chemical reactors has shown a significant increase in complexity of the models used during the last decades. This complexity increased the computational cost of the models demanding the development of efficient solution techniques. This paper discusses the implementation of an hp-adaptive refinement technique applied to a least-squares spectral element formulation as a mathematical framework for reactor modeling. The refinement is based on an estimate of the local Sobolev regularity index of the underlying solution by monitoring the decay rate of its Legendre expansion coefficients. The performance of the method is demonstrated numerically by using an analytical test case.