Efficient computation of ship’s wave-making resistance using michell’s integral

Abstract

The aim of the present paper is to find efficient method of computation the wave-making resistance of a ship using mitchell’s integral. The computational schemes described in publications suggest the use of simple quadratures (trapezoidal and Simpson’s rule) with a fixed number of integration’s intervals. This approach assumes manual setup of the algorithm for calculating the wave-making resistance for each new ship and makes it difficult to estimate the error of the obtained results. It is shown that the use of these simple quadratures makes it possible to obtain reliable results, but at the cost of tens of billions of calculations of the ship's surface function. The applicability of more advanced universal quadratures for calculating the mitchell’s integral is investigated: adaptive Newton-Cotes rules, Gauss-Kronrod rules and Clenshaw-Curtis quadratures. As a result, it is established that the Clenshaw-Curtis quadrature provides a reliable and efficient calculation of the mitchell’s integral. The computational scheme using this quadrature allows you to build an automatic algorithm for calculating the ship's wave-making resistance by type ship method.