TOWARDS A HIGHLY ACCURATE IMPLEMENTATION OF THE KIRCHHOFF APPROACH FOR COMPUTATIONAL AEROACOUSTICS

1996 ◽  
Vol 04 (02) ◽  
pp. 225-241 ◽  
Author(s):  
KRISTINE R. MEADOWS ◽  
H.L. ATKINS

This paper describes the development of high-order Kirchhoff algorithms and confirms that high-order accuracy can be achieved with the Kirchhoff approach when high-order integration and interpolation are properly implemented. This paper also establishes guidelines for enhancing accuracy of a given order property when the Kirchhoff formula is applied to results obtained from a computational fluid dynamics (CFD) solution. Accuracy is shown to increase when the Kirchhoff surface size is minimized. Reduction of the Kirchhoff surface size also enhances efficiency of the calculation because the size of the relatively expensive CFD computation is reduced. The accuracy of the Kirchhoff approach is also enhanced by increasing the density of information along the Kirchhoff surface. This increase in information is necessary because evaluation of the Kirchhoff integrand at the retarded time demands higher spatial resolution than the integration of the time-dependent nonlinear equations of the CFD calculation. A procedure has been developed that addresses the Kirchhoff resolution requirements without sacrificing efficiency. The error reduction realized with this procedure matches that realized with CFD mesh refinement, with almost no increase in cost.

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1555-1558
Author(s):  
JIAN XIA ◽  
CHAOQUN LIU

A new so-called truncation error reduction method (TERM) is developed in this work. This is an iterative process which initially uses a coarse grid (2h) to estimate the truncation error and then reduces the error on the original grid (h). The purpose of this method is to use multigrid technique to achieve high-order accuracy on simple stencils.


2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jia Guo ◽  
Huajun Zhu ◽  
Zhen-Guo Yan ◽  
Lingyan Tang ◽  
Songhe Song

By introducing hybrid technique into high-order CPR (correction procedure via reconstruction) scheme, a novel hybrid WCNS-CPR scheme is developed for efficient supersonic simulations. Firstly, a shock detector based on nonlinear weights is used to identify grid cells with high gradients or discontinuities throughout the whole flow field. Then, WCNS (weighted compact nonlinear scheme) is adopted to capture shocks in these areas, while the smooth area is calculated by CPR. A strategy to treat the interfaces of the two schemes is developed, which maintains high-order accuracy. Convergent order of accuracy and shock-capturing ability are tested in several numerical experiments; the results of which show that this hybrid scheme achieves expected high-order accuracy and high resolution, is robust in shock capturing, and has less computational cost compared to the WCNS.


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