A Positivity Preserving High-Order Finite Difference Method for Compressible Two-Fluid Flows*

Hyperbolicity, or the retention of a real-valued sound speed, is a required component

of any robust computational scheme for compressible flows.  In the context of two-fluid

compressible dynamics, strong shocks and large interfacial discontinuities are common

features that can easily induce positivity related failure in a simulation. A positivity

preserving algorithm is developed for a high-order, primitive variable based, weighted

essentially non-oscillatory (WENO) finite difference scheme. The positivity preservation

is accomplished by incorporating a flux limiting technique that locally adapts high order

fluxes towards first order to retain the physical bounds of the system without loss of

high order convergence. This positivity preserving scheme has been devised and

implemented up to 11th order in one and two dimensions for a two-fluid compressible

model that consists of a single mass, momentum, and energy equations, and

advection of material parameters for capturing the interfaces. Several one- and

twodimensional challenging test problems are conducted to validate its performance.

The scheme has been found to effectively retain high order accuracy while allowing for

the simulation of several challenging problems that otherwise could not be successfully

solved using the base scheme. The positivity-preserving algorithm allows computations

of challenging two-fluid problems without artificially smoothing the initial large interfacial

discontinuities, without any penalty on the CFL condition requirement, and without any

significant impact on the CPU times.