Lattice Boltzmann simulation of dispersion in two‐dimensional tidal flows

A lattice Boltzmann method (LBM) is applied to problems of dispersion in two‐dimensional water flows. The water flow is modelled by shallow water equations. A two‐distribution lattice Boltzmann equation algorithm is presented to solve the pollutant transport problem within the framework of shallow water flow. One distribution models the shallow water flow. The other distribution models the pollutant transport. Flow characteristics and concentration profiles of dispersive species are obtained at various flow regimes. For fast water flow, the concentration profiles are highly affected by the flow advection and become completely different from those at slow water flow. Numerical results are presented for pollutant transport in bounded and open channel flows. The proposed LBM is also used to simulate a pollution event in the Strait of Gibraltar. The obtained results indicate that the present method is useful for the investigation of transport phenomena by shallow water flows in complex geometries and practical flow problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Transient analysis of electro‐osmotic transport by a reduced‐order modelling approach

Transient behaviour of electro‐osmotic transport in typical electrokinetic channels is studied in this paper. The time needed for the electro‐osmotic flow to reach steady‐state exhibits multiple time scales depending on whether the flow is governed by either a viscous force, electrokinetic force or by a combination of both. When an intersection is present in the electrokinetic channel, such as in a cross or a T‐channel, the flow in the main channel and in the intersection gets to steady‐state at different times. A weighted Karhunen–Loève (KL) decomposition method is proposed in this paper to generate the global basis function for reduced‐order simulation. The key idea in a weighted KL approach is that, instead of minimizing a least‐squares measure of ‘error’ between the linear subspace spanned by the basis functions and the observation space, we minimize the weighted ‘error’ between the two spaces. The global basis functions in a weighted KL approach can be generated by computing the singular value decomposition (SVD) of the matrix containing the weighted snapshots. We show that the weighted KL decomposition based reduced‐order model is computationally more efficient and can capture the multiple time scales encountered in electro‐osmotic transport much more effectively compared to the classical KL decomposition based reduced‐order model. Copyright © 2003 John Wiley & Sons, Ltd.     

Numerical simulation of flapping wings using a panel method and a high‐order Navier–Stokes solver

The design of efficient flapping wings for human engineered micro aerial vehicles (MAVs) has long been an elusive goal, in part because of the large size of the design space. One strategy for overcoming this difficulty is to use a multifidelity simulation strategy that appropriately balances computation time and accuracy. We compare two models with different geometric and physical fidelity. The low‐fidelity model is an inviscid doublet lattice method with infinitely thin lifting surfaces. The high‐fidelity model is a high‐order accurate discontinuous Galerkin Navier–Stokes solver, which uses an accurate representation of the flapping wing geometry. To compare the performance of the two methods, we consider a model flapping wing with an elliptical planform and an analytically prescribed spanwise wing twist, at size scales relevant to MAVs. Our results show that in many cases, including those with mild separation, low‐fidelity simulations can accurately predict integrated forces, provide insight into the flow structure, indicate regions of likely separation, and shed light on design–relevant quantities. But for problems with significant levels of separation, higher‐fidelity methods are required to capture the details of the flow field. Inevitably high‐fidelity simulations are needed to establish the limits of validity of the lower fidelity simulations.Copyright © 2012 John Wiley & Sons, Ltd.     

A comparison of full non‐linear and reduced order aerodynamic models in control law design using a two‐dimensional aerofoil model

The prediction of the flutter boundary of an aircraft is a necessary but time consuming process, particularly as for the most realistic results a time accurate simulation of the interaction between the non‐linear aerodynamic and structural forces is required. Extension of the flight envelope by the design of active control laws to suppress flutter further increases the demands on computational time, to presently unrealistic levels. Use of a reduced order model (ROM) derived from, and in place of, the full non‐linear aerodynamics greatly reduces the time required for calculation of aerodynamic forces. However, this is necessarily accompanied by some loss in accuracy, and hence the method must be verified by comparison with results obtained by the full aerodynamic model before it may be used with confidence. Such a comparison is presented here, using a two‐dimensional aerofoil and control surface combination as a test case. Active control of the deflectable surface is used to attempt to increase the flutter speed across the complete Mach range, feedback control being achieved by gains acting on heave and pitch proportional and differential signals, interpreted as a hinge moment demand. Full non‐linear and reduced order aerodynamic models are then used to obtain optimum control law gain for flutter suppression. The results demonstrate that the ROM accurately predicts the open loop flutter boundary, gives a good approximation to the increase in flutter speed that may be produced by gain optimization, and produces a similar response given the identical gain values in each system for a significantly reduced cost. Copyright © 2005 John Wiley & Sons, Ltd.     

A coupled BEM and arbitrary Lagrangian–Eulerian FEM model for the solution of two‐dimensional laminar flows in external flow fields

This paper describes a new computational model developed to solve two‐dimensional incompressible viscous flow problems in external flow fields. The model based on the Navier–Stokes equations in primitive variables is able to solve the infinite boundary value problems by extracting the boundary effects on a specified finite computational domain, using the pressure projection method. The external flow field is simulated using the boundary element method by solving a pressure Poisson equation that assumes the pressure as zero at the infinite boundary. The momentum equation of the flow motion is solved using the three‐step finite element method. The arbitrary Lagrangian–Eulerian method is incorporated into the model, to solve the moving boundary problems. The present model is applied to simulate various external flow problems like flow across circular cylinder, acceleration and deceleration of the circular cylinder moving in a still fluid and vibration of the circular cylinder induced by the vortex shedding. The simulation results are found to be very reasonable and satisfactory. Copyright © 2001 John Wiley & Sons, Ltd.     

A domain decomposition method for a two‐phase transport model of polymer electrolyte fuel cell containing micro‐porous layer

In this paper, a nonlinear Dirichlet–Robin iteration‐by‐subdomain domain decomposition method is studied for a multidimensional, multiphysics, and multiphase model of polymer electrolyte fuel cell (PEFC) containing micro‐porous layer (MPL). Across the interface of gas diffusion layer and MPL in PEFC, it is well known that the capillary pressure is continuous, whereas liquid saturation is discontinuous, by which the liquid‐water removal in the porous electrodes can be significantly enhanced. We design a type of non‐overlapping domain decomposition method to deal with water transport in such multi‐layer diffusion media, where Kirchhoff transformation and its inverse techniques are employed to conquer the discontinuous and degenerate water diffusivity in the coexisting single‐phase and two‐phase regions. In addition, the conservation equations of mass, momentum, charge, and hydrogen and oxygen transport are also solved by the combined finite element–upwind finite volume method (FEM/FVM) to overcome the dominated convection effect in gas channels. Numerical simulations demonstrate that the presented techniques are effective in obtaining a fast and convergent nonlinear iteration for such a 3D PEFC model within around 50 steps, in contrast with the oscillatory and nonconvergent iteration conducted by standard FEM/FVM. A series of numerical convergence tests are also carried out to verify the efficiency and accuracy of the present numerical techniques. Copyright © 2012 John Wiley & Sons, Ltd.     

A cell‐based smoothed discrete shear gap method (CS‐FEM‐DSG3) based on the C0‐type higher‐order shear deformation theory for dynamic responses of Mindlin plates on viscoelastic foundations subjected to a moving sprung vehicle

A cell‐based smoothed discrete shear gap method (CS‐FEM‐DSG3) based on the first‐order shear deformation theory (FSDT) was recently proposed for static and dynamic analyses of Mindlin plates. In this paper, the CS‐FEM‐DSG3 is extended to the C⁰‐type higher‐order shear deformation plate theory (C⁰‐HSDT) and is incorporated with damping–spring systems for dynamic responses of Mindlin plates on viscoelastic foundations subjected to a moving sprung vehicle. At each time step of dynamic analysis, one four‐step procedure is performed including the following: (1) transformation of the weight of a four‐wheel vehicle into the sprung masses at wheels; (2) dynamic analysis of the sprung mass of wheels to determine the contact forces; (3) transformation of the contact forces into loads at nodes of plate elements; and (4) dynamic analysis of the plate elements on viscoelastic foundations. The accuracy and reliability of the proposed method are verified by comparing its numerical solutions with those of other available numerical results. Copyright © 2014 John Wiley & Sons, Ltd.     

A second‐order decoupled implicit/explicit method of the 3D primitive equations of ocean II: finite element spatial discretization

A fully discrete second‐order decoupled implicit/explicit method is proposed for solving 3D primitive equations of ocean in the case of Dirichlet boundary conditions on the side, where a second‐order decoupled implicit/explicit scheme is used for time discretization, and a finite element method based on the P₁(P₁) ? P₁?P₁(P₁) elements for velocity, pressure and density is used for spatial discretization of these primitive equations. Optimal H¹?L²?H¹ error estimates for numerical solution and an optimal L² error estimate for are established under the convergence condition of 0 < h≤β₁,0 < τ≤β₂, and τ≤β₃h for some positive constants β₁,β₂, and β₃. Furthermore, numerical computations show that the H¹?L²?H¹ convergence rate for numerical solution is of O(h + τ²) and an L² convergence rate for is O(h²+τ²) with the assumed convergence condition, where h is a mesh size and τ is a time step size. More practical calculations are performed as a further validation of the numerical method. Copyright © 2016 John Wiley & Sons, Ltd.