A component-based toolkit for simulating reacting flows with high order spatial discretisations on structured adaptively refined meshes

We present an innovative methodology for developing scientific and mathematical codes for computational studies of reacting flow, High-order (> 2) spatial discretisations are combined, for the first time, with multi-level block structured adaptively refined meshes (SAMR) to resolve regions of high gradients efficiently. Within the SAMR context, we use 4th order spatial discretisations to achieve the desired numerical accuracy while maintaining a shallow grid hierarchy. We investigate in detail the pairing between the order of the spatial discretisation and the order of the interpolant, and their effect on the overall order of accuracy. These new approaches are implemented in a high performance, component-based architecture (Common Component Architecture) and achieve software re-usability, flexibility and modularity. The high-order approach and the software design are demonstrated and validated on three test cases modelled as reaction-diffusion systems of increasing complexity. We also demonstrate that the 4th order SAMR approach can be computationally more economical compared to second-order approaches.