CONVERGENCE ANALYSIS FOR THE METHOD OF CHARACTERISTICS IN UNSTRUCTURED MESHES

A new conservative linear surface approximation (CLS) has been recently introduced to speed up the method of characteristic in unstructured meshes (MOC). In this work we present an analysis of convergence of the CLS that shows that, under optimal conditions, the method converges quadratically with the size of the regions, while the classical step characteristics approximation converges linearly. The predicted convergence rates apply only to a homogeneous convex domain with a regular boundary and analytical sources and are to be considered as an upper bound for realistic heterogeneous cases. We also analyze the errors induced by the numerical implementation of the CLS approximation and show their impact in the final error. Numerical calculations illustrate the convergence rates.