Optimized prefactored compact schemes for wave propagation phenomena

A new family of prefactored cost-optimized schemes is developed to minimize the computational cost for a given level of error in linear wave propagation applications, such as aerodynamic sound propagation. This work extends the theory of Pirozzoli to the prefactored compact high-order schemes of Hixon, which are MacCormack type schemes that use discrete Padé approximations. An explicit multi-step Runge-Kutta scheme advances the states in time. Theoretical predictions for spatial and temporal error bounds are used to drive the optimization process. Theoretical comparisons of the cost-optimized schemes with a classical benchmark scheme are made. Then, two numerical experiments assess the computational efficiency of the costoptimised schemes for computational aeroacoustic applications. A polychromatic sinusoidal test-case verifies that the cost-optimized schemes perform according to the design highorder accuracy characteristics for this class of problems. For this test case, upwards of a 50% computational cost-saving at the design level of error is recorded. The final test case shows that the cost-optimized schemes can give substantial cost savings for problems where a fully broadband signal needs to be resolved.

[1]  Massimiliano Guarrasia,et al.  Improvements for DFT Codes due to the Implementation of the 2 D Domain Decomposition Algorithm , 2013 .

[2]  Reda R. Mankbadi,et al.  Review of Computational Aeroacoustics Algorithms , 2004 .

[3]  R. Hixon,et al.  On Increasing the Accuracy of MacCprmack Schemes for Aeroacoustic Applications , 1997 .

[4]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[5]  R. Hixon.  Prefactored small-stencil compact schemes , 2000 .

[6]  C. Bogey,et al.  A family of low dispersive and low dissipative explicit schemes for flow and noise computations , 2004 .

[7]  Aldo Rona,et al.  Implementation of a high-order finite difference scheme to model wave propagation , 2007 .

[8]  M.Y. Hussaini,et al.  Low-Dissipation and Low-Dispersion Runge-Kutta Schemes for Computational Acoustics , 1994 .

[9]  Ning Li,et al.  2DECOMP&FFT - A Highly Scalable 2D Decomposition Library and FFT Interface , 2010 .

[10]  Matteo Bernardini,et al.  A general strategy for the optimization of Runge-Kutta schemes for wave propagation phenomena , 2009, J. Comput. Phys..

[11]  Aldo Rona,et al.  A selective overview of high-order finite-difference schemes for aeroacoustic applications , 2007 .

[12]  Eli Turkel,et al.  Compact Implicit MacCormack-Type Schemes with High Accuracy , 2000 .

[13]  C. Tam,et al.  Dispersion-relation-preserving finite difference schemes for computational acoustics , 1993 .

[14]  Graham Ashcroft,et al.  Optimized prefactored compact schemes , 2003 .

[15]  T. Colonius,et al.  Computational aeroacoustics: progress on nonlinear problems of sound generation , 2004 .

[16]  Sergio Pirozzoli,et al.  Performance analysis and optimization of finite-difference schemes for wave propagation problems , 2007, J. Comput. Phys..