This presentation shows part of the work done within the project ‘Advanced Numerical Simulation and Performance Evaluation of WAM-V ® in Spray Generating Conditions’ developed by the International Center for Numerical Methods in Engineering (CIMNE) under Navy Grant N62909-12-1-7101 issued by the Office of Naval Research Global.

One of the primary goals of that project was the development of a computational model for simulation of the Wave Adaptive Modular Vessel (WAM-V®) under spray generating conditions.

For this purpose, a Semi-Lagrangian Particle Finite Element Method (SL-PFEM) has been applied. This is the latest development within the framework of the so-called Particle Finite Element Method (PFEM), using the X-IVAS (eXplicit Integration along the Velocity and Acceleration Streamlines) scheme.

In this presentation we demonstrate the applicability of the SL-PFEM using the X-IVAS scheme for the simulation of the Wave Adaptive Modular Vehicle under spray generating conditions.


This presentation was held at the 31st Symposium on Naval Hydrodynamics on September 11-16th, 2016.

Draft García-Espinosa 273512028 2274 31st SNH.jpg


This study was partially supported by the WAM-V project funded under the Navy Grant N62909-12-1-7101 issued by Office of Naval Research Global, the SAFECON project (ref. 267521, FP7-IDEAS-ERC), the FORECAST project (ref. 664910, H2020-ERC-2014-PoC) and the X-SHEAKS project (ref. ENE2014-59194-C2-1-R). The United States Government has a royalty-free license throughout the world in all copyrightable material contained herein.

Permission to use the image shown in Figure 2 has been granted by Prof. Mehdi Ahmadian, VirginiaTech, USA. This image has appeared earlier in Andrew William Peterson’s Ph.D. thesis (2014), figure 3.12, page 55.


Becker, P., Idelsohn, S.R., Oñate, E.: A unified monolithic approach for multi-fluid flows and fluid–structure interaction using the Particle Finite Element Method with fixed mesh. Computational Mechanics, Vol. 55, Issue 6, June 2015, pp. 1091-1104. DOI 10.1007/s00466-014-1107-0.

Becker, P. An enhanced Particle Finite Element Method with special emphasis on landslides and debris flows. Ph.D. thesis, Barcelona Tech (2015).

Celledoni, E., Kometa, B.K., Verdier, O.: High Order Semi-Lagrangian Methods for the Incompressible Navier–Stokes Equations. Journal of Scientific Computing, Vol. 66, Issue 1, Jan. 2016, pp. 91-115. DOI 10.1007/s10915-015-0015-6

Courant, R., Friedrichs, K., Lewy, H.: On the Partial Difference Equations of Mathematical Physics. IBM Journal of Research and Development, Vol. 11, No. 2, 1967, pp. 215–234. DOI 10.1147/rd.112.0215.

Courant, R., Isaacson, E., Rees, M.: On the solution of nonlinear hyperbolic differential equations by finite differences. Communications on Pure and Applied Mathematics Vol. 5, No. 3, 1952, pp. 243–255. DOI 10.1002/cpa.3160050303.

Dadvand, P., Rossi, R., Oñate, E.: An Object-Oriented Environment for Developing Finite Element Codes for Multi-disciplinary Applications. Archives of Computational Methods in Engineering, Vol. 17, No. 3, 2010, pp. 253–297. DOI 10.1007/s11831-010-9045-2.

Dupont, T.F., Liu, Y.: Back and forth error compensation and correction methods for removing errors induced by uneven gradients of the level set function. Journal of Computational Physics, Vol. 190, No. 1, 2003, pp. 311–324. DOI 10.1016/S0021-9991(03)00276-6.

Dupont, T.F., Liu, Y.: Back and forth error compensation and correction methods for semi-lagrangian schemes with application to level set interface computations. Mathematics of Computation. Vol. 76, No. 258, 2007, pp. 647–669. DOI 10.1090/S0025-5718-06-01898-9.

Evans, M.W., Harlow, F.H.: “The Particle-in-Cell Method for Hydrodynamic Calculations”. LA-2139 Nov. 1957, Los Alamos National Laboratory, Los Alamos, New Mexico.

García-Espinosa, J., Oñate, E., Serván-Camas, B., Nadukandi, P. and Becker, P.A. “Advanced Numerical Simulation and Performance Evaluation of WAM-V ® in Spray Generating Conditions. Final Report. Navy Grant N62909-12-1-7101.” July 2015. CIMNE, Barcelona, Spain.

Gelet, R.M., Nguyen, G., Rognon, P.: Modelling interaction of incompressible fluids and deformable particles with the Material Point Method. In: The 6th International Conference on Computational Methods (ICCM2015) (2015)

García-Espinosa, J., Onate, E.: An unstructured finite element solver for ship hydrodynamics problems. Journal of Applied Mechanics Vol. 70, No. 1, 2003, pp. 18-26.

Harlow, F.H.: Hydrodynamic Problems Involving Large Fluid Distortions. Journal of the ACM, Vol. 4, No 2, 1957, pp. 137–142. DOI 10.1145/ 320868.320871.

Idelsohn, S.R., Marti, J., Becker, P., Oñate, E.: Analysis of multifluid flows with large time steps using the particle finite element method. International Journal for Numerical Methods in Fluids, Vol. 75, No 9, 2014, pp. 621–644.

Idelsohn, S.R., Nigro, N., Limache, A., Oñate, E.: Large time-step explicit integration method for solving problems with dominant convection. Computer Methods in Applied Mechanics and Engineering No. 217-220, 2012, pp. 168–185. DOI 10.1016/j.cma.2011.12.008.

Idelsohn, S.R., Nigro, N.M., Gimenez, J.M., Rossi, R., Marti, J.M.: A fast and accurate method to solve the incompressible Navier-Stokes equations. Engineering Computations Vol. 30, No. 2, 2013, pp. 197–222. DOI 10.1108/02644401311304854.

Idelsohn, S.R., Oñate, E., Del Pin, F.: The particle finite element method: a powerful tool to solve incompressible flows with freesurfaces and breaking waves. International Journal for Numerical Methods in Engineering, Vol. 61, No. 7, 2004, pp. 964–989. DOI 10.1002/nme.1096.

Idelsohn, S.R., Oñate, E., Nigro, N., Becker, P., Gimenez, J.: Lagrangian versus Eulerian integration errors. Computer Methods in Applied Mechanics and Engineering Vol. 293, 2015, pp. 191–206. DOI 10.1016/j.cma.2015.04.003.

MacCormack, R.W.: The Effect of Viscosity in Hypervelocity Impact Cratering. Journal of Spacecraft and Rockets Vol. 40, No. 5, 2003, pp. 757–763. DOI 10.2514/2.6901.

Min, C., Gibou, F.: A second order accurate projection method for the incompressible Navier-Stokes equations on non-graded adaptive grids. Journal of Computational Physics 219(2), 912–929 (2006). DOI 10.1016/j.jcp.2006.07.

Nadukandi, P.: Numerically stable formulas for a particle-based explicit exponential integrator. Computational Mechanics, Vol. 55, No. 5, 2015, pp. 903–920. DOI 10.1007/s00466-015-1142-5.

Nadukandi, P., Serván-Camas, B., Becker, P.A. and García-Espinosa, J., Seakeeping with the semi-Lagrangian Particle Finite Element Method. Published online in Computational Particle Mechanics (2016). DOI 10.1007/s40571-016-0127-2

Nielson, G.M., Jung, I.H.: Tools for computing tangent curves for linearly varying vector fields over tetrahedral domains. IEEE Transactions on Visualization and Computer Graphics, Vol. 5, No. 4, 1999, pp. 360–372. DOI 10.1109/2945.817352.

Onate, E., García-Espinosa, J., Idelsohn, S. R. “Ships Hydrodynamics”. In Stein, de Borst and Hughes (eds.), Encyclopedia of computational mechanics. John Wiley & Sons, 2004. DOI: 10.1002/ 0470091355.ecm070

Peterson, A.W.: Simulation and Testing ofWave-Adaptive Modular Vessels. Ph.D. thesis, Virginia Polytechnic Institute and State University (2014).

Robert, A.: A stable numerical integration scheme for the primitive meteorological equations. Atmosphere-Ocean, Vol. 19, No. 1, 1981, pp. 35-46. DOI 10.1080/07055900.1981.9649098.

Sawyer, J.S.: A semi-Lagrangian method of solving the vorticity advection equation. Tellus, Vol. 15, No. 4, 1963, pp. 336–342. DOI 10.1111/j.2153-3490.1963.tb01396.x.

Selle, A., Fedkiw, R., Kim, B., Liu, Y., Rossignac, J.: An Unconditionally Stable MacCormack Method. Journal of Scientific Computing. Vol. 35, No. 2-3, 2008, pp. 350–371. DOI 10.1007/s10915-007-9166-4.

Sulsky, D., Zhou, S.J., Schreyer, H.L.: Application of a particle-in-cell method to solid mechanics. Computer Physics Communications. Vol. 87, No. 1-2, 1995, pp. 236–252. DOI 10.1016/0010-4655(94)00170-7.

WAM-V: The Wave Adaptive Modular Vessel. URL http://www.wam-v.com

Zhang, D.Z., Zou, Q.,VanderHeyden,W.B., Ma, X.: Material point method applied to multiphase flows. Journal of Computational Physics, Vol. 227, No. 6, 2008, pp. 3159–3173. DOI 10.1016/ j.jcp.2007.11.021.

Back to Top

Document information

Published on 08/08/17
Submitted on 08/08/17

Licence: CC BY-NC-SA license

Document Score


Views 33
Recommendations 0

Share this document

claim authorship

Are you one of the authors of this document?