Efficient methods with higher order interpolation and MOOD strategy for compressible turbulence simulations

Efficient higher order interpolation schemes based on a multi-dimensional optimal order detection (MOOD) paradigm are developed coupled with the implicit time discretization scheme and further investigated for implicit large eddy simulation of compressible turbulence. The developed methodology utilizes higher-order either the upwind or the central interpolation to minimize numerical dissipation and meantime hybridizes shock capturing scheme that is also provided with higher-order interpolation to stabilize the solution. Simple and effective technique is proposed to apply the current method to an unsteady dual-time stepping scheme, which is to the best of the authors' knowledge the first time to develop the strategy for the MOOD application within an unsteady implicit time discretization framework. The resulting schemes are implemented in the simplified finite volume method that is constructed on non-uniform, curvilinear, multiblock structured grids. Numerical results for a comprehensive suite of both benchmark and practical problems demonstrate that the designed schemes simultaneously obtain the well-resolved broadband turbulence and the sharp shock profiles with considerable reduction in the computation cost.