Bingham, Harry B.

Engsig-Karup, Allan Peter

Lindberg, Ole

Madsen, Per A.

We present recent and preliminary work directed towards the development of a simplified, physics-based model for improved simulation of ship-ship interaction that can be used for both analysis and real-time computing (i.e. with real-time constraints due to visualization). The goal is to implement the model into a large maritime simulator for training of naval officers, in particular tug boat helmsmen. Tug boat simulators are used for training of communication and situation awareness during manoeuvre involved with towing of large vessels. A main objective of the work is to improve and enable more accurate (realistic) and much faster ship-wave and ship-ship simulations than are currently possible. The coupling of simulation with visualization should improve the visual experience such that it can be perceived as more realistic in training. Today the state-of-art in real-time ship-ship interaction is for efficiency reasons and time-constraints in visualization based on model experiments in towing tanks and precomputed force tables. We anticipate that the fast, and highly parallel, algorithm described by Engsig-Karup et al. [2011] for execution on affordable modern high-throughput Graphics Processing Units (GPUs) can provide the basis for efficient simulations in combination with an accurate free-surface model for Ship-Ship simulation. Another area of application is the determination of wave disturbances from a ship in a coastal environment, channels and harbours. The model proposed in the following can in a simple and efficient way calculate the wave field from a ship sailing in a finite depth sea, even with variations in the height of sea bed. The generated wave field can be applied as an input to other models that simulate the marine environment on a larger scale

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Downloaded from orbit.dtu.dk on: Dec 20, 2017Towards Real Time Simulation of Ship-Ship InteractionLindberg, Ole; Bingham, Harry B.; Engsig-Karup, Allan Peter; Madsen, Per A.Published in:International Workshop on Water Waves and Floating BodiesPublication date:2012Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Lindberg, O., Bingham, H. B., Engsig-Karup, A. P., & Madsen, P. A. (2012). Towards Real Time Simulation ofShip-Ship Interaction. In International Workshop on Water Waves and Floating BodiesThe 27th International Workshop on Water Waves and Floating BodiesIWWWFB 2012April 22-25, 2012, Copenhagen, DenmarkTowards Real Time Simulation of Ship-Ship Interaction∗Ole Lindberg Harry B. BinghamDTU Mechanical Engineering DTU Mechanical EngineeringDK-2800 Kgs. Lyngby DK-2800 Kgs. LyngbyDenmark DenmarkEmail: olli@mek.dtu.dk Email: hbb@mek.dtu.dkAllan P. Engsig-Karup Per A. MadsenDTU Informatics DTU Mechanical EngineeringDK-2800 Kgs. Lyngby DK-2800 Kgs. LyngbyDenmark DenmarkEmail: apek@imm.dtu.dk Email: prm@mek.dtu.dkWe present recent and preliminary work directed towards the development of a simplified,physics-based model for improved simulation of ship-ship interaction that can be used for bothanalysis and real-time computing (i.e. with real-time constraints due to visualization). Thegoal is to implement the model into a large maritime simulator for training of naval officers, inparticular tug boat helmsmen. Tug boat simulators are used for training of communication andsituation awareness during manoeuvre involved with towing of large vessels. A main objective ofthe work is to improve and enable more accurate (realistic) and much faster ship-wave and ship-ship simulations than are currently possible. The coupling of simulation with visualization shouldimprove the visual experience such that it can be perceived as more realistic in training. Todaythe state-of-art in real-time ship-ship interaction is for efficiency reasons and time-constraintsin visualization based on model experiments in towing tanks and precomputed force tables. Weanticipate that the fast, and highly parallel, algorithm described by Engsig-Karup et al. [2011] forexecution on affordable modern high-throughput Graphics Processing Units (GPUs) can providethe basis for efficient simulations in combination with an accurate free-surface model for Ship-Ship simulation. Another area of application is the determination of wave disturbances from aship in a coastal environment, channels and harbours. The model proposed in the following canin a simple and efficient way calculate the wave field from a ship sailing in a finite depth sea,even with variations in the height of sea bed. The generated wave field can be applied as aninput to other models that simulate the marine environment on a larger scale.Ship-Wave ModelIn order to take full advantage of the accuracy and efficiency of the wave model discussedabove, we will adopt a rough approximation of the ship geometry based on surface pressuredistributions. This will of course limit the accuracy of the geometric description of the hull.The representation of sailing ships by a pressure distribution on the free surface is a classical∗We wish to thank Force Technology, DTU Mechanical Engineering and DTU Informatics for funding thisproject and the Danish Center for Scientific Computing for providing supercomputing resources.idea that dates back at least to Thomson (Lord Kelvin) [1910]. Many applications of the ideaexist in the literature, including e.g. recent work by Raven [2010], who used the idea for hulloptimization based on wave-making resistance; and Li and Sclavounos [2002] who used surfacepressures to study nonlinear solitary waves in shallow water as a model for a ship moving atsub-critical, critical and super-critical speed. To model a ship as a pressure distribution onthe free surface, the hull must be approximated by a single-valued function of the horizontalcoordinates: ηship = ηship(t, x, y). Ship appendices like bulbous bows or complex rudder tubescan not be represented and must be suitably smoothed out. The fluid pressure on the ship hullsurface is the sum of the dynamic and the hydrostatic components. Clearly an approximationto the stationary ship is obtained by applying the hydrostatic component pship = ρgηship. Asthe ship begins to move, the flow induced dynamic components must be balanced by the appliedsurface pressure in order to maintain a constant hull form. The goal of this project is to finda robust means of predicting and applying this pressure in general, but we present here somepreliminary work with constant applied pressures. The model is based on assuming inviscid,incompressible and irrotational potential flow. The free surface of the sea is described by thesingle-valued function η = η(t, x, y), where t is time and (x, y) the horizontal coordinates. Massconservation is satisfied though the Laplace equation for the scalar velocity potential∇2φ = 0, z ∈ [−h, η], (1)where z is the vertical coordinate and h = h(x, y) is the distance from the mean sea level tothe sea bed. The motion of the free surface is governed by the kinematic free surface boundarycondition∂η∂t+ u · ∇η = w, z = η, (2)where u = ∇φ ∈ R2 is the horizontal velocity vector and w is the vertical free surface velocity.The forces on the free surface are governed by the dynamic free surface condition∂φ∂t+12u · u+pρ+ gη = 0, z = η, (3)where p is the pressure, ρ ≈ 1000kg/m3 is the density and g = 9.81m/s2 is the gravitationalacceleration. The equations are solved in a moving reference frame attached to the ship andgiven by (τ, xm, ym), where xm is forward and ym is the transverse direction relative to the ship.The ship is assumed not to move in the vertical direction and to be sailing in the the positivex direction. Based on these assumptions the coordinate transform from the fixed to the shipfollowing frame of reference isτ = t, xm = x− V t, ym = y, zm = z, (4)where V = const. is the ship velocity in the x direction. The coordinate transform adds aconvective term to the kinematic and dynamic free surface boundary conditions∂η∂τ− V∂η∂xm+ u · ∇η = w, z = η, (5)∂φ∂t− V∂φ∂xm+12u · u+pρ+ gη = 0, z = η. (6)The free surface boundary conditions are are solved in a ship following rectangular domain onthe free surface and the Laplace equation is solved in a corresponding domain extending to theseabed, i.e. the solution domain isΩ = {[xm, ym, zm]T ∈ R3 : xm,min ≤ xm ≤ xm,max, ym,min ≤ ym ≤ ym,max, h ≤ zm ≤ η} (7)Figure 1: The Kelvin wave system generated by a moving pressure distribution with the param-eters Fn(ship) = 0.30, Fn(depth) = 0.47, B/L = 0.2 and D/L = 0.04. The semi analyticalsolution are below the center line and the numerical solutions are above the center line.The numerical solutions ηh ≈ η and φh ≈ φ are represented by local polynomials on a structuredgrid over the free surface boundary of Ω. The equations are transformed from the physical do-main to a time independent computational domain, where the derivatives are approximated byhigher-order finite differences. The temporal derivatives are approximated by the classical ex-plicit fourth-order Runge-Kutta method. Details on the numerical approximations and solutionmethods are described by Engsig-Karup et al. [2009].ApplicationsIn this preliminary work, the method has been tested on the double cosine "ship" geometry usedin Li and Sclavounos [2002] where the pressure distribution isp(xm, ym) = ρgD cos2(pixmL)cos2(piymB), −L2≤ xm ≤L2, −B2≤ ym ≤B2, (8)with D the draft, L the length and B the width of the "ship". The preliminary simulationshave been promising and a snap shot illustrating a generated Kelvin Wave system is presentedin Figure 1. The calculation are shown next to the far-field linear as expressed for example byWehausen and Laitone [1960]. This semi-analytical solution has been used to find the theo-retical wave system caused by the double cosine pressure distribution above and we present aqualitative comparison between this and out numerical solution to the linear problem in figure1. The result is qualitatively in good agreement and we are now working on making a morequantitative comparison. The second application is a typical cargo ship. The ship geometry hasbeen simplified such that the surface of the hull is described by a single valued function of thehorizontal coordinates: The bulbous bow has been extended upwards through the free surface,the vertical sides of the hull have been mollified and sharp intersections between the still waterlevel and the hull has been smoothed. The resultant wave system is seen in Figure 2.ConclusionThe Kelvin wave system has been simulated around a ship propagating at subcritical fixedspeed in still water using a potential flow model with linearized free surface boundary conditions.Figure 2: The wave system generated by the hydro static pressure on a typical cargo ship sailingwith at Froude numbers Fn(ship) = 0.20 and Fn(depth) = 0.32. The geometric parameters ofthe ship are B/L = 0.13 and D/L = 0.04.Preliminary results have been presented for a simple pressure patch which show good qualitativeagreement with the semi-analytic solution. Future work will focus on including the nonlinearterms in the free-surface boundary conditions, and using the dynamic pressure on the ship hullto achieve a fixed geometry. The model will be implemented for parallel execution on modernhigh-throughput Graphics Processing Units (GPUs) and implemented in a real marine simulatorto predict ship-ship interaction effects in real time.AcknowledgementWe would like to thank Ingrid Marie Vincent Andersen for providing the ship hull sections.ReferencesA. P. Engsig-Karup, H. B. Bingham, and O. Lindberg. An efficient flexible-order model for 3dnonlinear water waves. Journal of Computational Physics, 228:2100–2118, 2009.A. P Engsig-Karup, M. G. Madsen, and S. L. Glimberg. A massively parallel gpu-acceleratedmodel for analysis of fully nonlinear free surface waves. Accepted for publication in Int. J.Num. Methods in Fluids, 2011.Y. Li and P. D. Sclavounos. Three-dimensional nonlinear solitary waves in shallow watergenereated by an advancing disturbance. J. Fluid Mech., 470:383–410, 2002.H. C. Raven. Validation of an approach to analyse and understand ship wave making. Journalof Maritime Science and Technology, 15:331–344, 2010.William Thomson (Lord Kelvin). On ship waves. In Collected Works, pages 270–306. Cambridge,1910.J. V. Wehausen and E. V. Laitone. Surface waves. In Handbuch der Physik, pages 446–778.Springer, 1960.

Towards Real Time Simulation of Ship-Ship Interaction

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Towards Real Time Simulation of Ship-Ship Interaction

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