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Summary The paper addresses a numerical approach for solving the Baer‐Nunziato equations describing compressible 2‐phase flows. We are developing a finite‐volume method where the numerical flux is approximated with the Godunov scheme based on the Riemann problem solution. The analytical solution to this problem is discussed, and approximate solvers are considered. The obtained theoretical results are applied to develop the discrete model that can be treated as an extension of the Rusanov numerical scheme to the Baer‐Nunziato equations. Numerical results are presented that concern the method verification and also application to the deflagration‐to‐detonation transition (DDT) in porous reactive materials.

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A computational uid dynamics (CFD) technique is employed to study hypersonic high-enthalpy air ows around blunt bodies with the purpose of predicting convective heat transfer on the body surface for a range of ow velocities relevant to suborbital ight of re-entry vehicles such as the Space Shuttle Orbiter (USA), and the Buran (Russia). The method uses Park's two-temperature model for the description of thermochemical nonequilibrium processes in high-temperature air and solves the full Navier-Stokes equations for a model of multicomponent reacting gas mixture in the ÿnite volume formulation. The calculations performed in this research are intended to simulate some experiments carried out in the high-energy shock tunnels of the DLR, Germany, and the CALSPAN, USA, where the heat ux distribution over a model surface was measured at several freestream conditions related to the range of velocities mentioned above. The main emphasis is on comparing numerical and experimental results in order to verify adequacy of the heat ux data predicted by the CFD technique for suborbital ight speeds of re-entry vehicles.

SUMMARY We develop an Eulerian fixed grid numerical method for calculating multi‐material fluid flows. This approach relates to the class of interface capturing methods. The fluid is treated as a heterogeneous mixture of constituent materials, and the material interface is implicitly captured by a region of mixed cells that have arisen owing to numerical diffusion. To suppress this numerical diffusion, we propose a composite Riemann problem (CRP), which describes the decay of an initial discontinuity in the presence of a contact point between two different fluids, which is located off the initial discontinuity point. The solution to the CRP serves to calculate multi‐material no mixed numerical flux without introducing any material diffusion. We discuss the CRP solution and its implementation in the multi‐material fluid Godunov method. Numerical results show that a simple framework of the CRP greatly improves capturing material interfaces in the Godunov method and reproduces many of the advantages of more complicated interface tracking multi‐material treatments. Copyright © 2014 John Wiley & Sons, Ltd.