Implementation of Fast Fourier Transforms and Integral Equation Theories towards calculating Virial Coefficients
Sankararaman, Srihari Gangaikondan
MetadataShow full item record
The virial equation of state is a power series of the compressibility factor in terms of density. The calculation of the coefficients has been the focus of this study. In this work, we look to exploit the use of the Fast Fourier Transform (FFT) to the maximum extent and reduce the cost of implementing Mayer Sampling Monte Carlo (MSMC). Fast Fourier Transform is nearly instantaneous to perform and is accurate to at least the sixth decimal place. In this work, we go about creating an algorithm into two pools of cluster diagrams – one implementing FFT and the other implementing MSMC. Applying this new algorithm, we are able to calculate the higher order virial coefficients more quickly. This method has proved effective in making the calculation speed faster and more accurate. This work also looks into calculating virial coefficients using the integral equation theory approximations. We have automated the process of building the cluster diagram pertaining to the Percus-Yevick and hypernetted chain approximation of the integral equation theories. The integral values of these approximations were also calculated using Fast Fourier Transform.