ObjectiveThe Objective is to develop an embedded boundary method under an adaptive mesh refinement framework to compute low and high Mach number compressible Navier Stokes equations in arbitrary complex time dependent geometries on two and three dimensional computational domains.

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We discuss the effect on the transient dynamics of the Richtmyer-Meshkov instability due to small-scale perturbations introduced by a set of solid circular cylinders located along the material interface. The arrangement of the cylinders mimics (in a twodimensional domain) the presence of the solid supporting grid wires used in the formation of the material interface in an experimental setup. The numerical experiments are performed by utilizing an embedded boundary-Adaptive mesh refinement method. We quantify the effect of introducing the cylinders on the mixing layer growth and the mixedness level, and qualitatively demonstrate the effect of the perturbation introduced by the cylinders on the mixing layer structure. We empirically model the effect of the solid cylinders based on their diameter, and find that the effect of the cylinders on the mixing layer growth is a linear function of the cylinder diameter. The linear model allows us to predict the change in the mixing layer growth within a ±10% range, except for very small ratios of the initial perturbation amplitude of the density interface to the cylinder diameter.

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We present an embedded ghost-fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. The PDE multidimensional extrapolation approach of Aslam [1] is used to reconstruct the solution in the ghost-fluid regions and impose boundary conditions at the fluid-solid interface. The CNS equations are numerically solved by the second order multidimensional upwind method of Colella [2] and Saltzman [3]. Block-structured adaptive mesh refinement implemented under the Chombo framework is utilized to reduce the computational cost while keeping high-resolution mesh around the embedded boundary and regions of high gradient solutions. Numerical examples with different Reynolds numbers for low and high Mach number flow will be presented. We compare our simulation results with other reported experimental and computational results. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.