Application of the simplified eigenstructure decomposition solver to the simulation of general multifield models

Phase Appearance or Disappearance in Two-Phase Flows

“…One of the reasons for the large oscillations of the interpolation polynomial P exact is the presence of a cluster of intermediate eigenvalues near 0, which are very close to each other and which are 4 orders of magnitude smaller than the extremal eigenvalues (see (2.40)). In [23], an approximate Roe matrix is generated by treating this cluster of eigenvalues like a single eigenvalue (the largest of them). The method of [23] provides comparable results to the usual Roe method in standard situations.…”

“…In [23], an approximate Roe matrix is generated by treating this cluster of eigenvalues like a single eigenvalue (the largest of them). The method of [23] provides comparable results to the usual Roe method in standard situations. Inspired by this work, we generate an approximate polynomial which interpolates the extremal eigenvalues λ min , λ max and only one of the intermediate eigenvalues, the largest one, denoted by λ max int (as well as its opposite −λ max int for symmetry reasons).…”