Numerical stability in multifluid gas dynamics with implicit drag forces

The numerical stability of a conventional explicit numerical scheme for solving the inviscid multifluid dynamical equations describing a multicomponent gas mixture is investigated both analytically and computationally. Although these equations do not explicitly contain diffusion terms, it is well known that they reduce to a single-fluid diffusional description when the drag coefficients in the species momentum equations are large. The question then arises as to whether their numerical solution is subject to a diffusional stability restriction on the time step in addition to the usual Courant sound-speed stability condition. An analytical stability analysis is performed for the special case of a quiescent binary gas mixture with equal sound speeds and temperatures. It is found that the Courant condition is always sufficient to ensure stability, so that no additional diffusional stability restriction arises for any value of the drag coefficient, however large. This result is confirmed by one-dimensional computational results for binary and ternary mixtures with unequal sound speeds, which remain stable even when the time step exceeds the usual diffusional limit by factors of order 100.