Error analysis for 1D propagation using Eigen Analysis in General Curvilinear Coordinates

Hawkins, Rhiannon and Wilson, Alexander G. (2021) Error analysis for 1D propagation using Eigen Analysis in General Curvilinear Coordinates. In AIAA 2021. Aerospace Research Central.. (doi:10.2514/6.2021-2298).

Abstract

This paper provides a formal error analysis for acoustic propagation in one-dimension using the Eigen Analysis in General Curvilinear Coordinates (EAGCC) method. The method is shown to be second order accurate in mesh spacing. Different errors are observed in the forward and reverse direction relative to the input wave and equations have been derived that describe the error in each direction. They are composed of three leading order terms related to the first, second, and third derivatives of the Jacobian matrix with respect to distance in the direction of propagation. The EAGCC method has been successfully applied to a number of real engineering applications in three dimensions, but this is the first time a formal error analysis has been attempted. Although the analysis is in one dimension, a discussion is provided regarding the application of the results to three dimensional meshes. The analysis is supported by a range of numerical test-cases which confirm the predicted relationship between the wavenumber and mesh related parameters, and the error. It is demonstrated that local numerical errors act as sources of noise, such that the global error can be calculated as the cumulative effect of all of the local errors along the duct.

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