The paper presents implicit large-eddy simulation (ILES) simulation of a shock tube experiment involving compressible turbulent mixing. A new characteristic-based approximate Riemann solver is derived, and employed in a second-order and fifth-order finite volume Godunov-type ILES framework. The methods are validated against (qualitative) experimental data and then compared and contrasted in terms of resolved turbulent kinetic energy and mixing parameters as a function of grid resolution. It is concluded that both schemes represent the experiment with good accuracy. However, the fifth-order results are approximately equivalent to results gained on double the grid size at second order, whereas the fifth-order method requires only approximately 20% extra computational time.
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