Cartesian method, which in some places is mentioned as Volume-Tracking Method, is one of the popular methods used in simulating transient flow problems involving complex moving boundaries. It has the advantage of being time-saving, efficient and robust for certain types of fluid-structure interaction problems. This method is featured by a Cartesian background Euler mesh discretizing the flow domain and a moving surface cutting through it. The most critical operation of this method is treating the cells cut by the moving boundaries accurately and stably. When the Cartesian methods are applied, the temporal discretization of the governing equations of the flow can be either implicit or explicit. For simulations cases in which time-accurately capturing wave propagation or flow evolution is essential, explicit approach still plays an important role among the researchers and currently available simulation codes. The current study is focused on the numerical performances of the explicit type of Cartesian methods when applied on the compressible flow cases. The accuracy of the simulation results, stability and grid-convergence problems resulted from a moving, impermeable boundary cutting through the background mesh are addressed. Example problems include the one-dimensional piston problem and the expanding sphere flow problems. In one case the sphere expands supersonically thus a spherical shock is generated. In another case it expands at a subsonic speed and works as a monople impulse noise source. To the best knowledge of the author, the problem of expanding-sphere generated acoustic impulse has not been reported anywhere else. Simple theoretical analyses are included and results of numerical experiments are reported.

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