On the Accuracy of Direct Noise Calculations Based on the Euler Model

Abstract

The paper reviews a class of Direct Noise Calculation (DNC) models based on the compressible Euler equations and analyses their computational accuracy considering the combination of model completeness, scheme accuracy and stability to round off errors. It is shown that a form of the Nonlinear Disturbance Equations (NLDE) is sensitive to the round off errors. An NLDE formulation with Roe average matrix (NLDE/Roe) for minimizing the round off errors is proposed. (The NLDE/Roe is identical to Direct Numerical Simulation (DNS) at rather large solutions and converges to the Linearised Euler Equations (LEE) at the small solutions NLDE/Roe thus accurately treats the signals including both large and small scales of disturbances). A version of NLDE in the case of disturbance decomposition is given in the general form. While studying the DNC model efficiency, a new measure of the total model accuracy is introduced. It is proposed to test all the models and schemes available by comparing the output numerical result with the exact solution of the complete model, that is, with the Euler equations.