Revisit to the THINC/QQ scheme: Recent progress to improve accuracy and robustness

Abstract In this article, we revisit to the THINC/QQ (tangent of hyperbola interface capturing method with quadratic surface representation and Gaussian quadrature) scheme to make thorough investigations on its numerical property. Furthermore, it presents some recent progress made extensively on THINC/QQ algorithm to improve numerical accuracy and robustness which include (1) construct the interface equation on the global coordinate so as to apply THINC/QQ on polygonal/polyhedral elements, which ensures the boundedness of numerical solutions as well; (2) determine the coefficients of reconstruction polynomial from the unit normal vector of interface to reduce computational cost and alleviate numerical diffusion; (3) represent the interface with a cubic polynomial rather than quadratic representation used in THINC/QQ to obtain better geometric fidelity; (4) provide an appropriate choice considering different combinations, such as the number of quadrature points and temporal discretization methods. The verification benchmark tests are carried out on different types of grids, which convinces that THINC/QQ scheme with normalization on global coordinate delivers higher accuracy and robustness than the original one, and demonstrates effective competition compared with other existing interface capturing methods.