MAE Department - PG Seminar - THINC: a practical general-purpose reconstruction scheme for CFD

Reconstructions are needed in building up numerical schemes for computational fluid dynamics. Different reconstruction functions have their strength and weakness for a given profile.

This presentation focuses on a Sigmoid function with single-degree freedom. The reconstruction, so-called THINC (Tangent of Hyperbola for INterface Capturing) scheme, employs the hyperbolic tangent function to fit initially the jump-like profile, which is commonly observed in the solutions of the interface between multi-phase flows, the contact discontinuity and the shock wave in compressible fluid. As the discontinuous solution is well close to a hyperbolic function with a sharp transition layer, a THINC reconstruction resembles a jump-like solution perfectly. Recalling that THINC function also retrieves a quasi-piece-wise constant when a very flatten transit layer is reconstructed, the THINC reconstruction can be used as a general-purpose reconstruction building block in CFD (Computational Fluid Dynamics).

The multi-dimensional THINC function allows the transitional layer to be a polynomial higher than quadratic order, varieties and more difficult reconstructions can be built in structured and unstructured meshes, so as to make the THINC method be even more competitive in capturing spatial complexity. The THINC scheme plays a versatile rule in the CFD. Some examples will be shown in the presentation.