The χ-schemes: a new consistent high-resolution formulation based on the normalized variable methodology Original Research Article

This paper deals with the formulation and testing of a new class of consistent high-resolution schemes, denoted as the χ-schemes. These schemes, combine consistency, accuracy and boundedness across systems of equations and are suitable for use in the simulation of multi-phase and multi-component flows. The consistency feature refers to the capability of these schemes to implicitly satisfy the additional algebraic constraint representing a global conservation relation governing certain sets of equations (e.g., species mass fraction, volume fraction, etc.). Four χ-schemes are implemented within an unstructured grid finite-volume framework, tested by solving four multi-component pure-advection test problems, and shown to be consistent.