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.

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The ignition is still unachieved in current schemes of inertial confinement fusion (ICF) despite significant efforts in this direction. The reason for it is unclear as the dynamics of target combine a lot of physical processes that are crucial for successful ignition. One possible limiting factor is known for a long time – hydrodynamic instabilities and mixing. Current work consider the effect of initial roughness on compression efficiency of ICF targets. The roughness is set on the ice–ablator boundary (outer ice interface). First, some analytical results on stability of accelerated perturbed interface are presented. Second, numerical simulations of ICF target show the influence of initial perturbations on hot–spot conditions and ice–ablator mixing.

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The problem of high velocity impact between two solid plates where one of them has a non-uniformly disturbed density field is studied. The nature of an initial perturbation here differs from one considered in the classical Richtmyer–Meshkov instability (RMI). We consider the instability that develops from the initial perturbations of the density field with a flat interface between plates, while RMI is triggered by a shock passing through the corrugated interface. The structure of perturbation fields generated in the plates due to impact and the interface evolution are studied via the analytic linear and nonlinear models for normal modes using the Euler equations for compressible fluids and appropriate boundary conditions. Such analysis reveals three different regimes in which the generated disturbances can develop depending on the direction of the perturbation wave vector. The obtained theoretical findings are in good quantitative agreement with our detailed numerical simulations.

The paper addresses a novel interface-capturing approach for two-phase flows governed by the five-equation diffuse interface model. To suppress the numerical diffusion of the interface, we introduce a primitive sub-cell reconstruction based on volume fractions in neighbouring cells. This reconstruction gives rise to a Riemann problem (CRP) with an additional contact discontinuity, so-called composite Riemann problem, which is stated on mixed cell faces. The CRP solution is used to calculate the numerical flux across cell faces of mixed cells with taking into account the interface reconstructed patterns. A hybrid HLL-HLLC method is incorporated to approximate the solution of the CRP. The proposed approach is shown to effectively reduce the interface numerical diffusion without introducing spurious oscillations. Its performance and robustness is examined by 1D and 2D numerical tests.

Abstract. In the present paper we consider an Eulerian numerical method for