Coupling of CFD model and FVCOM to predict small-scale coastal flows

9th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China

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2010, 22(5), supplement :284-289 DOI: 10.1016/S1001-6058(09)60208-0

Coupling of CFD model and FVCOM to predict small-scale coastal flows Xiu-guang Wu 1,2, Han-song Tang 2,* 1

2

Zhejiang Inst. of Hydraulics & Estuary, Hangzhou, China Dept. of Civil Eng., City College, City Univ. of New York, New York, NY 10031, USA * E-mail: [email protected]

ABSTRACT : In order to accurately simulate small-scale coastal ocean phenomena, we propose to couple a computational fluid dynamics (CFD) model with the Unstructured Grid Finite Volume Coastal Ocean Model (FVCOM). The CFD model resolves small-scale flows, the FVCOM predicts large-scale background currents, and the resulting hybrid system is able to capture flow phenomena with spatial scales from centimeters to hundreds of kilometers. The coupling is two-way and realized using domain decomposition with aid of Chimera overset grids. Numerical examples are presented to demonstrate the feasibility and performance of the proposed hybrid approach. KEY WORDS: Multi-scale; Coastal ocean flow; CFD; FVCOM; Chimera overset grids.

1 INTRODUCTION It is now becoming more and more urgently needed to accurately predict small-scale coastal ocean flows encountered in emerging issues such as environmental recovery, coastal cleanup, and military operations. Nevertheless, this is a great challenge in view of the fact that the efforts using numerical simulation of coastal ocean flows have been greatly successful but, until now, merely at large-scale phenomena. The challenge comes from model restrictions, numerical techniques, and computer capabilities [1-2]. For instance, a deep ocean circulation model has difficulty in dealing with the vertical mesh when bathymetry changes abruptly at continental slopes as well as smaller scales of nearshore currents [3-4]. Limitations such as hydrostatic assumptions and/or twodimensionality of coastal models are inherent restrictions that prohibit them to appropriately simulate many important phenomena such as vertical motions of Langmuir circulations. In recent years,

computational fluid dynamics (CFD) approaches, which solve the full Navier-Stokes equations and can accurately model small-scale and detailed flow structures, are now applied to flows with large ranges of scales [5]. In principle, CFD approaches have no such limitations and can capture flow phenomena at various scales. Nevertheless, they are prohibitively expensive and not applicable in simulating actual coastal ocean flows. Since there is strong interaction between small- and large-scale phenomena, a multi-scale/multi-physics approach is indispensible for an accurate simulation of small-scale coastal flows, and it is becoming a trend in prediction of coastal ocean flows in recent years [6-7]. It is commonly recognized that real success of a single, comprehensive model capable of dealing with smallscale problems is unlikely in the near future. Nevertheless, given the fact that numerical modeling has reached the point where the simulation of flows of individual scales and phenomena has become mature, the hybrid method (HM), together with domain decomposition method (DDM), is one of the most promising currently available techniques to bridge the scales and overcome the inherent restrictions in smallscale modeling. By HM and DDM, a flow domain will be divided into many subdomains, and each of them is assigned to an individual model, which is coupled with others used for the neighbor subdomains. We propose to simulate small-scale coastal ocean flow by coupling CFD and coastal models using HM and DDM with Chimera overset grids [8]. The former is designed to capture small-scales, and the latter is employed to predict large-scale background currents.

9th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China As a sequel to the authors’ previous paper [8], this article further discusses the proposed approach and presents more numerical results. In particular, a threedimensional (3D), unsteady, incompressible CFD model is coupled with the Unstructured Grid Finite Volume Coastal Ocean Model (FVCOM), and more detailed coupling techniques and solutions are described. The feasibility and performance of the proposed approach is illustrated in simulation of thermal effluent released from discharge ports with diameters in order of centimeters into a river with kilometer in width, and the simulations results are compared with those obtained with a pure CFD approach. In addition, modeling of the thermal discharge into a coastal flow setting is presented, together with discussions on further development of the proposed hybrid approach. 2 CFD MODEL AND FVCOM The CFD model employed in this paper solves unsteady, 3D, incompressible Navier-Stokes equations, and it is enhanced with domain decomposition to deal with complex geometry [9-12]. The model has been tested and applied in various problems from academe as well as industry, such as vortex breakdown and flow past bridge piers [12-13]. In the CFD model, the governing equations are discretized using a secondorder-accurate, implicit, finite-volume method on nonstaggered grids, and they are solved using a dual timestepping artificial compressibility method. A fourthdifference artificial dissipation method is employed to eliminate odd–even decoupling of the pressure field. The discretized system is integrated using an implicit, pressure-based pre-conditioner enhanced with the local-time-stepping and V-cycle multigrid method to accelerate convergence. A DDM approach using Chimera overset grids is implemented by which the flow domain is divided into subdomains arbitrarily overlapping with each other and is covered by structured, body-fitted, curvilinear grids. Two-way coupling is enforced between subdomains, and Schwartz alternative iteration is employed [14]. In order to achieve seamless transition of solutions between subdomains, an effective mass conservation algorithm is proposed [9]. In the FVCOM, the flow domain is discretized using a triangle mesh on horizontal planes and a layer mesh in the vertical direction. The governing equations are discretized using a finite volume method, and the model has a two-dimensional (2D) external mode and a 3D internal mode. The convection terms are discretized using second-order accurate upwind schemes, and Runge-Kutta methods are used to march in time. In the solution procedure, first, the external

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mode is solved to obtain water surface elevation and depth averaged velocities in horizontal directions. Second, in the internal mode, solving the momentum equations provides horizontal velocity distributions, which are then adjusted according to the horizontal velocities obtained in the external mode. The vertical velocity component is obtained using the continuity equation in the internal mode. In order to maintain consistency between the internal and external modes, the vertical velocity is modified to ensure mass conservation at every time step. The external and internal modes may have different time steps. Details for the FVCOM can be found in [15-16]. 3 COPLING OF CFD MODEL AND FVCOM In this paper, the CFD model is employed to resolve small-scale flow phenomena, and the FVCOM is used to model background circulations. The solution domains of CFD model and FVCOM overlap over a region (Fig. 1). As a coupling strategy, the 3D CFD model is coupled to the 3D internal mode of the FVCOM, and the two models exchange solutions for the velocity distributions at grid interfaces between them. The strategy is based on the assumption that the horizontal velocity distributions in the vertical direction do not directly affect water surface elevation and averaged values of the horizontal velocities determined by the external mode, which is consistent with the assumption in the FVCOM [15].

Fig. 1 Schematic representation of CFD model and FVCOM coupling

Chimera overset grids overlap arbitrarily with each other, and they provide the best possible flexibility in connecting different models. In this research, Chimera overset grids are used between CFD model and FVCOM, as shown in Fig. 2. In the figure, a-a and b-b are grid interfaces for CFD model and FVCOM, respectively, and interpolation to find the solutions at the grid nodes on the interfaces is necessary to

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facilitate the solution exchange between the two models. In order to find host cells (within CFD grids) for grid nodes on b-b, a search procedure described in [17] is employed. Similar methods are employed in

will be left for future study. 4 NUMERICAL EXAMPLES Numerical examples of the proposed HM approach and the coupling techniques are presented to demonstrate their feasibility and performance. The first example is thermal effluent discharged from a diffuser into a rectangle channel (Fig. 3). The diffuser consists of a pipe and 10 discharge ports on it. The pipe is 1.32 m in diameter, it lies on the channel bottom with an angle of 110 degree to the flow direction, and its offshore end is 201 m away from the left bank. The discharge ports are 0.175 in diameter, and they have different upward angles gradually

Fig. 2 Coupling of CFD and FVCOM with Chimera overset grid in horizontal directions. Solid line – FVCOM grid, dash line – CFD grid

finding the host elements within the FVCOM grid (triangle mesh in horizontal directions) for nodes on grid interface a-a of the CFD model. It is noted that the host element (within the grid of FVCOM) of an interface node on a-a does not change in horizontal plane in simulation of the flow. However, in view that FVCOM uses σ coordinate in the vertical direction, the host cells (within CFD grid) and host elements (within FVCOM grid), respectively for nodes on b-b and a-a, may change as water surface elevation changes (unsteady flow). As a result, the relative positions of CFD and FVCOM grids change during modeling, the host cells and elements of interface grids on a-a and b-b are subject to change, and they need to be located at each time step during the simulation. The solution at nodes on b-b is obtained by a tri-linear interpolation from their host elements [17]. A linear interpolation is employed to implement solution update from the host elements onto grid nodes on a-a. The solution exchange between FVCOM and CFD model, or, the interpolation of the solution at the nodes on a-a and b-b, has second-order accuracy, which is consistent with the accuracy of the both models. The coupling is two-way and implemented using the Schwarz alternative procedure in the iteration between the two models [14]. In order to achieve correct as well as accurate solutions at grid interfaces, mass conservation needs consideration in interpolation from FVCOM model to CFD. It is anticipated that our previous effective algorithm can be implemented for this purpose [9, 17]. However, this

Fig. 3 Thermal effluent into river and computational mesh. a) River configuration and diffuser location. b). Mesh for CFD (structured grid) and FVCOM (unstructured grid, bounded with red lines). c) Diffuser and ports and their CFD mesh

9th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China changing from 45o to 18o from no. 1 to 10 ports (Fig. 3c). The ambient flow is 0.3 m/s in velocity and 20.5 o C in temperature at the entrance and 16 m in depth at the exit. The effluent discharge at the port mouths is 3.92 m/s in velocity and 32.0 oC in temperature. Multiple layers of grids are used to fully resolve the diffuser configuration, and each port has a few grid nodes across their diameters. The CFD model has a

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mesh with 180,000 nodes. For details on the diffuser and the mesh arrangement, the readers are referred to [5]. The FVCOM model uses 11 layers of grids in the vertical direction with the total 115,000 nodes on each layer. The flow is also simulated by only using the CFD model with 220,000 nodes. The computed flow field is presented in Fig. 4. It is seen from Fig. 4a that in the coupling approach, solution runs across grid interfaces smoothly, and CFD and FVCOM provide similar contours at the overlapped region, which are in reasonable agreement with those obtained only by CFD approach (Fig. 4b). Fig. 4c and 4d indicate that the coupling hybrid approach and CFD model provide similar temperature solutions. The discrepancy between the hybrid CFD/FVCOM and CFD approaches is mainly attributed to the fact that they use different conditions. For instance, the former has a slip velocity condition at the lateral walls and uses a free surface, whereas the latter employs no-slip condition at the lateral walls and a rigid surface. The second example is the thermal discharge with configurations and dimensions same to those in the

Fig. 4 Solution for thermal effluent discharged into river. Total velocity contours (m/s) on a horizontal plane 3m above the ground. (a) Total velocity by CFD/FVCOM coupling. Dash contour line – FVCOM, solid contour line – CFD, red border line – FVCOM boundary, black border line – CFD boundary. (b) Total velocity by CFD. (c) Temperature by CFD/FVCOM coupling. (d) Temperature by CFD

Fig. 5 Thermal Effluent discharge in coastal flow. Top – bathymetry, mesh, and CFD model location, bottom – zoom in mesh

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previous example but into New York coastal settings (Fig. 5). The diffuser is located at the mouth of Hudson River, and the thermal effluent is affected by the tides. The flow is simulated using the CFD and FVCOM hybrid approach, and the computed solutions for the flow around the diffuser are presented in Fig. 6. Fig. 6a shows the flow velocity distribution and streamlines on a plane 3m above the ground under flood tide condition, and it is clearly seen that the flow structures can smoothly pass the interfaces between CFD model and FVCOM. Fig. 6b illustrates the corresponding computed 3D view of the thermal discharge plume, together with its discharge ports.

accurate, and robust coupling between CFD model and FVCOM, further study on related issues such as conservation at interfaces between the models and a systematical numerical experiment on the coupling strategies and algorithms are necessary. These tasks will be left for our future efforts. ACKNOWLEDGEMENT This research is supported by PSC CUNY and NSFC (40806037). Valuable input from Dr. C. S. Chen at Univ. of Massachusetts Dartmouth is acknowledged. REFERENCES [1] Griffles S M, Boning C, Bryan F O, et al. Developments in ocean climate modeling, Ocean Modelling. 2000(2): 123– 192. [2] Dolbow J, Khaleel M A, Mitchell J. Multiscale Mathematics – Initiative, A Roadmap. PNNL-14966, 2004. [3] Song Y T, Hou, Y T. Parametric vertical coordinate formulation for multiscale, Boussinesq, and nonBoussinesq ocean modeling, Ocean Modeling. 2006(11): 298-332. [4] Heimusund B –O, Berntsen J. On a class of ocean model instability that may occur when applying small time steps, implicit methods, and low viscosities, Ocean Modeling. 2004(7): 135-144. [5] Tang H S, Paik J, Sotiropoulos F, et al. Three-dimensional CFD modeling of thermal discharge from multports. ASCE J Hyd. Eng. 2008(134): 1210-1224.

Fig. 6 Coastal flow solution. Top – total velocity at a horizontal plane (black line – CFD boundary, red line – FVCOM boundary), bottom – 3D thermal plume

5 CONCLUSIONS This paper discusses simulation of small-scale coastal flows using CFD and FVCOM hybrid approach. In particular, DDM with Chimera overset grids is employed to couple CFD and FVCOM models, and coupling strategies are described. The numerical examples demonstrate the feasibility and promising capability of the approach. In order to achieve correct,

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9th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China [14] Schwarz H A. Uber einige abbildungsaufgaben, GES. Abh. 1869(11): 65-83. [15] Chen C, Liu H, Beardsley R C. An unstructured, finitevolume, three-dimensional, primitive equation ocean model: application to coastal ocean and estuaries, J Atm & Oceanic Tech. 2003(20): 159-186. [16] Chen C S, Beardsley R C, Geoffrey C. An Unstructured Grid, Finite-Volume Coastal Ocean Model FVCOM User

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Manual. SMAST/UMASSD-06-0602, 2006. [17] Tang H S. Study on a grid interface algorithm for solutions of incompressible Navier-Stokes equations, Computers & Fluids. 2006(35):1372-1383.