Swarm Intelligence Approach for Rational Global Approximation of Characteristic Curves for the Van der Waals Equation of State

The Van der Waals (VdW) equation of state is a popular generalization of the law of ideal gases proposed time ago. In many situations, it is convenient to compute the characteristic curves of the VdW equation of state, called binodal and spinodal curves. Typically, they are constructed through data fitting from a collection of data points represented in the two-dimensional pressure-volume plane. However, the resulting models are still limited and can be further enhanced. In this paper, we propose to extend this polynomial approach by using a rational function as a fitting function. In particular, we consider a rational free-form Bézier curve, which provides a global approximation to the shape of the curve. This rational approach is more flexible than the polynomial one owing to some extra parameters, the weights. Unfortunately, data fitting becomes more difficult as these new parameters have also to be computed. In this paper we address this problem through a powerful nature-inspired swarm intelligence method for continuous optimization called the bat algorithm. Our experimental results show that the method can reconstruct the characteristic curves with very good accuracy.