ORIGINAL ARTICLE Prediction of hydrodynamic coefficients of ship hulls by high-order Godunov-type methods Andrea Di Mascio Æ Riccardo Broglia Æ Roberto Muscari Received: 12 July 2007 / Accepted: 15 May 2008 / Published online: 5 August 2008 Ó JASNAOE 2008 Abstract Numerical simulations of incompressible flows, with and without free surface, by means of high-order Godunov-type schemes are presented; the results are compared with the second-order essentially nonoscillatory (ENO) scheme, already implemented and extensively used by the authors for the simulation of flows around ship hulls. Uncertainty assessment and convergence properties are discussed for two practical test cases: the steady and unsteady laminar flow past a NACA 0012 profile with and without incidence, and the steady free surface flow past a ship hull at model Reynolds number. The analysis is aimed to highlight advantages and drawbacks of the numerical schemes considered herein. Keywords Godunov schemes  High-order schemes  Naval hydrodynamics List of symbols q generic dependent variable ~ q Fourier transform of q Z Fourier symbol x circular frequency q i q at point x i Dx space step Dt time step Re Reynolds number Fr Froude number We Weber number F x T x-component of the total nondimensional force F x p x-component of the pressure contribution to the total force C T total resistance coefficient h/h f grid ratio r observed converged order RE Richardson extrapolation 1 Introduction Godunov-type schemes were introduced in the early 1980s in the field of compressible flow simulation as a general- ization to high order of accuracy for the original Godunov [1] scheme that was only first-order accurate. They gained increasing success because of their ability to deal with both discontinuous solutions (shocks and contact discontinu- ities) with oscillations bounded by a term of the order of the truncation error [2], as well as smooth regions of flow, where they are able to attain high accuracy. The application of these schemes to the computation of incompressible flows in the framework of the pseudo- compressibility formulation (Chorin [3]) can be found, for instance, in Di Mascio et al. [4, 5], for free surface flows in the naval context. Both a free surface fitting algorithm and a surface capturing (level set) approach were used with a second-order essentially nonoscillatory (ENO) scheme (Harten et al. [2]), in conjunction with a very effective multigrid algorithm. This work was presented in part at the International Conference on Computational Methods in Marine Engineering—MARINE 2007, Barcelona, June 3–4, 2007. A. Di Mascio (&)  R. Broglia  R. Muscari Istituto Nazionale per Studi ed Esperienze di Architettura Navale, via di Vallerano, 139-00128 Rome, Italy e-mail: a.dimascio@insean.it R. Broglia e-mail: r.broglia@insean.it R. Muscari e-mail: r.muscari@insean.it 123 J Mar Sci Technol (2009) 14:19–29 DOI 10.1007/s00773-008-0021-6