A compatible Lagrangian hydrodynamic scheme for multicomponent flows with mixing

Numerical stability in multifluid gas dynamics with implicit drag forces

“…The calculations were found to remain stable even when the time step exceeds the diffusional limit by factors of order 100. This behavior is consistent with previous computational experience [16] and strongly suggests that the present analytical stability results are more general than their derivation, and that numerical schemes of this type are not subject to diffusional stability conditions, in spite of the fact that the equations become diffusional in form and character for large β.…”

“…Eqs. (16) and (17) will be approximated by means of a widely used standard finite-difference numerical scheme for the solution of compressible flow problems [23,24]. The scheme is explicit except that the drag term is treated implicitly to avoid the corresponding explicit stability condition [24,25], which becomes onerous when β is large.…”

“…The initial conditions for both calculations were p i = x m p and T m = 1000 K, where p = 0.1 atm and the initial mole fractions x m were defined by x Ar = 1 − x He = x/L in the binary mixture, and by x Ne = 1/3 and x Ar = 2/3 − x He = (2/3)x/L in the ternary mixture. The drag coefficients β mn were obtained from the turbulent mixing model of Scannapieco and Cheng [15,16], and have the form…”

“…Equations of this type are widely used in plasma physics [1][2][3][4][5], multiphase flow [6][7][8][9][10], and other areas. A particular physical application of timely interest is the quantitative description of material mixing [11][12][13][14][15][16][17], which is important in combustion, inertial confinement fusion, and certain astrophysical problems, inter alia.…”

“…However, the multifluid equations remain valid and can still be solved in their general form even when the drag coefficients are large, provided the drag terms are treated implicitly to avoid the unacceptably restrictive explicit stability condition that would otherwise be incurred [16,24,25]. As will be seen, however, the implicit treatment of the drag terms actually results in an explicit treatment of the corresponding diffusion terms in the large-friction limit, and therefore would not be expected to remove or alleviate the associated diffusional stability condition.…”