On hyperbolization of a single-pressure gas suspension model

For a model of a single-pressure multivelocity multicomponent heterogeneous mixture consisting of several gases and one incompressible component, a hyperbolization method is presented based on introducing a parameter $\xi$ into the model equations. A characteristic analysis of the modified model equations is carried out, and their hyperbolicity for parameter values $\xi\in(0,1]$ is established. It is shown that the spurious motion of some mixture components is suppressed with a suitable choice of $\xi$. The hyperbolic system of equations is integrated using the multidimensional nodal method of characteristics, which is based on splitting the original system into one-dimensional subsystems, each solved by applying the inverse method of characteristics. This approach is used to compute several one- and two-dimensional test problems.