An adaptive artificial viscosity method for quintic spline reconstruction scheme

In this paper, an adaptive artificial viscosity approach for quintic spline reconstruction (QSR) scheme is proposed to adjust the artificial viscosity coefficient dynamically. This approach is devised from the dispersion property of QSR scheme, in which the artificial viscosity coefficient increases as dispersion error between the modified scaled wavenumber of QSR scheme and the spectral scaled wavenumber increases. To establish the relationship between the flow field and the modified scaled wavenumber, the scale sensor is introduced and used to identify the effective scaled wavenumber of flow field. The effective scaled wavenumber can approximate the modified scaled wavenumber of QSR scheme very well in the range of low and middle wavenumber regions, which is proved by Fourier analysis in spectral space and numerical tests with fixed and variable frequencies. When the effective scaled wavenumber is identified, whether the flow field can be resolved by the QSR scheme is confirmed, and the artificial viscosity coefficient is then determined by the adaptive criterion, which is constructed according to the numerical tests and data fitting experiments. The adaptive artificial viscosity approach is verified effectively in several benchmark cases, and the results demonstrate the good performance of this adaptive method.