A non-oscillatory balanced scheme for an idealized tropical climate model

We use the non-oscillatory balanced numerical scheme developed in Part I to track the dynamics of a dry highly nonlinear barotropic/baroclinic coupled solitary wave, as introduced by Biello and Majda (2004), and of the moisture fronts of Frierson et al. (2004) in the presence of dry gravity waves, a barotropic trade wind, and the beta effect. It is demonstrated that, for the barotropic/baroclinic solitary wave, except for a little numerical dissipation, the scheme utilized here preserves total energy despite the strong interactions and exchange of energy between the baroclinic and barotropic components of the flow. After a short transient period where the numerical solution stays close to the asymptotic predictions, the flow develops small scale eddies and ultimately becomes highly turbulent. It is found here that the interaction of a dry gravity wave with a moisture front can either result in a reflection of a fast moistening front or the pure extinction of the precipitation. The barotropic trade wind stretches the precipitation patches and increases the lifetime of the moisture fronts which decay naturally by the effects of dissipation through precipitation while the Coriolis effect makes the moving precipitation patches disappear and appear at other times and places.     

High-order targeted essentially non-oscillatory scheme for two-fluid plasma model

The weakly ionized plasma flows in aerospace are commonly simulated by the single-fluid model, which cannot describe certain nonequilibrium phenomena by finite collisions of particles, decreasing the fidelity of the solution. Based on an alternative formulation of the targeted essentially non-oscillatory(TENO) scheme, a novel high-order numerical scheme is proposed to simulate the two-fluid plasmas problems. The numerical flux is constructed by the TENO interpolation of the solution and its deri...     

Development and assessment of a variable-order non-oscillatory scheme for convection term discretization

A new scheme for convection term discretization is developed, called VONOS (variable-order non-oscillatory scheme). The development of the scheme is based on the behaviour of well-known non-oscillatory schemes in the pure convection of a step profile test case. The new scheme is a combination of the QUICK and BSOU (bounded second-order upwind) schemes. These two schemes do not have the same formal order of accuracy and for that reason the formal order of accuracy of the new scheme is variable. The scheme is conservative, bounded and accurate. The performance of the new scheme was assessed in three test cases. The results showed that it is more accurate than currently used higher-order schemes, so it can be used in a general purpose algorithm in order to save computational time for the same level of accuracy. © 1998 John Wiley & Sons, Ltd.     

Experiments with three-dimensional riblets as an idealized model of shark skin

The skin of fast sharks exhibits a rather intriguing three-dimensional rib pattern. Therefore, the question arises whether or not such three-dimensional riblet surfaces may produce an equivalent or even higher drag reduction than straight two-dimensional riblets. Previously, the latter have been shown to reduce turbulent wall shear stress by up to 10%. Hence, the drag reduction by three-dimensional riblet surfaces is investigated experimentally. Our idealized 3D-surface consists of sharp-edged fin-shaped elements arranged in an interlocking array. The turbulent wall shear stress on this surface is measured using direct force balances. In a first attempt, wind tunnel experiments with about 365,000 tiny fin elements per test surface have been carried out. Due to the complexity of the surface manufacturing process, a comprehensive parametric study was not possible. These initial wind tunnel data, however, hinted at an appreciable drag reduction. Subsequently, in order to have a better judgement on the potential of these 3D-surfaces, oil channel experiments are carried out. In our new oil channel, the geometrical dimensions of the fins can be magnified 10 times in size as compared to the initial wind tunnel experiments, i.e., from typically 0.5 mm to 5 mm. For these latter oil channel experiments, novel test plates with variable fin configuration have been manufactured, with 1,920–4,000 fins. This enhanced variability permits measurements with a comparatively large parameter range. As a result of our measurements, it can be concluded, that 3D-riblet surfaces do indeed produce an appreciable drag reduction. We found as much as 7.3% decreased turbulent shear stress, as compared to a smooth reference plate. However, in direct comparison with 2D riblets, the performance of 3D-riblets is still inferior by about 1.7%. On the other hand, it appears conceivable, with a careful design of the fin shape (possibly supported by theory), that this inferiority in performance might be reduced. Nevertheless, at present, it seems to be rather unlikely, that 3D-riblets can significantly outperform 2D-riblets. Finally, one interesting finding remains to be mentioned: The optimum drag reduction for short 3D-riblets occurs at a lower rib height than for longer 3D-riblets or for infinitely long 2D-riblets. The same observation had been made previously on shark scales of different species with differing rib lengths, but no explanation could be given. Received: 1 March 1999/Accepted: 16 July 1999     

A reduced-order flow model for vocal fold vibration: From idealized to subject-specific models

We present a reduced-order model for fluid–structure interaction (FSI) simulation of vocal fold vibration during phonation. This model couples the three-dimensional (3D) tissue mechanics and a one-dimensional (1D) flow model that is derived from the momentum and mass conservation equations for the glottal airflow. The effects of glottal entrance and pressure loss in the glottis are incorporated in the flow model. We consider both idealized vocal fold geometries and subject-specific anatomical geometries segmented from the MRI images of rabbits. For the idealized vocal fold geometries, we compare the simulation results from the 1D/3D hybrid FSI model with those from the full 3D FSI simulation based on an immersed-boundary method. For the subject-specific geometries, we incorporate previously estimated tissue properties for individual samples and compare the results with those from the high-speed imaging experiment of in vivo phonation. In both setups, the comparison shows good agreement in the vibration frequency, amplitude, phase delay, and deformation pattern of the vocal fold, which suggests potential application of the present approach for future patient-specific modeling.     

A new matrix dissipation model for central scheme

In this paper, a simple and efficient improvement to the famous Swanson–Turkel matrix dissipation model for the central scheme is proposed. In the new matrix dissipation model, the accuracy is improved by eliminating the second‐difference dissipation added to the characteristic fields representing the vorticity waves. This strategy is proposed based on analyzing the flow‐physics about shock‐vortex interaction using the Rankine–Hugoniot jump condition. In this paper, the behavior of central scheme for rotational flow is also theoretically and numerically analyzed. Results show a newfound problem of the original scalar and matrix dissipation models, in which for rotational flow excessive second‐difference dissipation is added due to the pressure‐based shock sensor. With current new matrix dissipation model improved accuracy is obtained at minimal cost overhead, especially, in the highly vortical region where the second‐difference dissipation is reduced. At the same time, it preserves the excellent shock capturing capability and convergence speed of original method. Numerical properties of this new matrix dissipation model are validated with a series of numerical experiments and results comparison with original model verifies improved performance of current method. Copyright © 2013 John Wiley & Sons, Ltd.     

Flow behavior and deposition study of pollen-shape carrier particles in an idealized inhalation path model

Pollen-shape (spiked sphere) hydroxyapatite (HA) particles for drug carrier application are studied. The particle shape and size effect on flow characteristics and deposition are assessed. The pollen-shape HA particles are synthesized to have comparable size as typical carrier particles with mean diameter of 30-50 m and effective density less than 0.3 g/cm 3 . The flow behaviors of HA and commonly used lactose (LA) carrier particles are characterized by the Carr's compressibility index (CI). The HA particle...     

A new well‐balanced Hermite weighted essentially non‐oscillatory scheme for shallow water equations

Hermite weighted essentially non‐oscillatory (HWENO) methods were introduced in the literature, in the context of Euler equations for gas dynamics, to obtain high‐order accuracy schemes characterized by high compactness (e.g. Qiu and Shu, J. Comput. Phys. 2003; 193 :115). For example, classical fifth‐order weighted essentially non‐oscillatory (WENO) reconstructions are based on a five‐cell stencil whereas the corresponding HWENO reconstructions are based on a narrower three‐cell stencil. The compactness of the schemes allows easier treatment of the boundary conditions and of the internal interfaces. To obtain this compactness in HWENO schemes both the conservative variables and their first derivatives are evolved in time, whereas in the original WENO schemes only the conservative variables are evolved. In this work, an HWENO method is applied for the first time to the shallow water equations (SWEs), including the source term due to the bottom slope, to obtain a fourth‐order accurate well‐balanced compact scheme. Time integration is performed by a strong stability preserving the Runge–Kutta method, which is a five‐step and fourth‐order accurate method. Besides the classical SWE, the non‐homogeneous equations describing the time and space evolution of the conservative variable derivatives are considered here. An original, well‐balanced treatment of the source term involved in such equations is developed and tested. Several standard one‐dimensional test cases are used to verify the high‐order accuracy, the C‐property and the good resolution properties of the model. Copyright © 2010 John Wiley & Sons, Ltd.     

A well‐balanced weighted essentially non‐oscillatory scheme for pollutant transport in shallow water

In this paper, a well‐balanced finite difference weighted essentially non‐oscillatory scheme is presented for modeling transport and diffusion of pollutant in shallow water flows. The scheme balances exactly the flux gradients and the source terms. Extensive one‐dimensional and two‐dimensional numerical experiments on uniform and curvilinear meshes strongly suggest that high resolution results are achieved for both water depth and pollutant concentration. The scheme is efficient and robust and can be applied to practical numerical simulation of pollutant transport phenomena in shallow water flows. Copyright © 2012 John Wiley & Sons, Ltd.     

Well‐balanced discontinuous Galerkin method and finite volume WENO scheme based on hydrostatic reconstruction for blood flow model in arteries

The blood flow model in arteries admits the steady state solutions, for which the flux gradient is nonzero, and is exactly balanced by the source term. In this paper, by means of hydrostatic reconstruction, we construct a high order discontinuous Galerkin method, which exactly preserves the dead‐man steady state, which is characterized by a discharge equal to zero (analogue to hydrostatic equilibrium). Moreover, the method maintains genuine high order of accuracy. Subsequently, we apply the key idea to finite volume weighted essentially non‐oscillatory schemes and obtain a well‐balanced finite volume weighted essentially non‐oscillatory scheme. Extensive numerical experiments are performed to verify the well‐balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.     

Assessment of an unstructured exponential scheme discrete ordinates radiation model for non-gray media

For radiative transfer in complex geometries, Sakami and his co-workers have developed a discrete ordinates method (DOM) exponential scheme for unstructured meshes which was mainly applied to gray media. The present study investigates the application of the unstructured exponential scheme to a wider range of non-gray scenarios found in fire and combustion applications, with the goal to implement it in an in-house Computational Fluid Dynamics (CFD) code for fire simulations. The original unstructured gray exponential scheme is adapted to non-gray applications by employing a statistical narrow-band/correlated-k (SNB-CK) gas model and meshes generated using the authors’ own mesh generator. Different non-gray scenarios involving spectral gas absorption by H₂O and CO₂ are investigated and a comparative analysis is carried out between heat flux and radiative source terms predicted and literature data based on ray-tracing and Monte Carlo methods. The maximum discrepancies for total radiative heat flux do not typically exceed 5%.     

A mixed finite element scheme for viscoelastic flows with XPP model

A mixed finite element formulation for viscoelastic flows is derived in this paper, in which the FIC （finite incremental calculus） pressure stabilization process and the DEVSS （discrete elastic viscous stress splitting） method using the Crank-Nicolson-based split are introduced within a general framework of the iterative version of the fractional step algorithm. The SU （streamline-upwind） method is particularly chosen to tackle the convective terms in constitutive equations of viscoelastic flows. Thanks to the proposed scheme the finite elements with equal low-order interpolation approximations for stress-velocity-pressure variables can be successfully used even for viscoelastic flows with high Weissenberg numbers. The XPP （extended Pom-Pom） constitutive model for describing viscoelastic behaviors is particularly integrated into the proposed scheme. The numerical results for the 4：1 sudden contraction flow problem demonstrate prominent stability, accuracy and convergence rate of the proposed scheme in both pressure and stress distributions over the flow domain within a wide range of the Weissenberg number, particularly the capability in reproducing the results, which can be used to explain the ＂die swell＂ phenomenon observed in the polymer injection molding process.     

A semi-implicit finite volume scheme for a simplified hydrostatic model for fluid-structure interaction

Simulating fluid-structure interaction problems usually requires a considerable computational effort. In this article, a novel semi-implicit finite volume scheme is developed for the coupled solution of free surface shallow water flow and the movement of one or more floating rigid structures. The model is well-suited for geophysical flows, as it is based on the hydrostatic pressure assumption and the shallow water equations. The coupling is achieved via a nonlinear volume function in the mass conservation equation that depends on the coordinates of the floating structures. Furthermore, the nonlinear volume function allows for the simultaneous existence of wet, dry and pressurized cells in the computational domain. The resulting mildly nonlinear pressure system is solved using a nested Newton method. The accuracy of the volume computation is improved by using a subgrid, and time accuracy is increased via the application of the theta method. Additionally, mass is always conserved to machine precision. At each time step, the volume function is updated in each cell according to the position of the floating objects, whose dynamics is computed by solving a set of ordinary differential equations for their six degrees of freedom. The simulated moving objects may for example represent ships, and the forces considered here are simply gravity and the hydrostatic pressure on the hull. For a set of test cases, the model has been applied and compared with available exact solutions to verify the correctness and accuracy of the proposed algorithm. The model is able to treat fluid-structure interaction in the context of hydrostatic geophysical free surface flows in an efficient and flexible way, and the employed nested Newton method rapidly converges to a solution. The proposed algorithm may be useful for hydraulic engineering, such as for the simulation of ships moving in inland waterways and coastal regions.     

A well‐balanced stable generalized Riemann problem scheme for shallow water equations using adaptive moving unstructured triangular meshes

We propose a well‐balanced stable generalized Riemann problem (GRP) scheme for the shallow water equations with irregular bottom topography based on moving, adaptive, unstructured, triangular meshes. In order to stabilize the computations near equilibria, we use the Rankine–Hugoniot condition to remove a singularity from the GRP solver. Moreover, we develop a remapping onto the new mesh (after grid movement) based on equilibrium variables. This, together with the already established techniques, guarantees the well‐balancing. Numerical tests show the accuracy, efficiency, and robustness of the GRP moving mesh method: lake at rest solutions are preserved even when the underlying mesh is moving (e.g., mesh points are moved to regions of steep gradients), and various comparisons with fixed coarse and fine meshes demonstrate high resolution at relatively low cost. Copyright © 2013 John Wiley & Sons, Ltd.     

A boundary element application for mixed modeloading idealized sawtooth fracture surface

In this paper, a 2-D elastic-plastic BEM formulation predicting the reduced mode IIand the enhanced mode I stress intensity factors are presented. The dilatant boundary conditions (DBC) are assumed to be idealized uniform sawtooth crack surfaces and an effective Coulombsliding law. Three types of crack face boundary conditions, i.e. (1) BEM sawtooth model-elasticcenter crack tip; (2) BEM sawtooth model-plastic center crack tip; and (3) BEM sawtoothmodel-edge crack with asperity wear are presented. The model is developed to attempt todescribe experimentally observed non-monotonic, non-linear dependence of shear crack behavioron applied shear stress, superimposed tensile stress, and crack length. The asperity sliding isgoverned by Coulombs law of friction applied on the inclined asperity surface which hascoefficient of friction μ. The traction and displacement Greens functions which derive fromNaviers equations are obtained as well as the governing boundary integral equations for an infiniteelastic medium. Accuracy test is performed by comparison stress intensity factors of the BEMmodel with analytical solutions of the elastic center crack tip. The numerical results show thepotential application of the BEM model to investigate the effect of mixed mode loading problemswith various boundary conditions and physical interactions.     

Exactly well‐balanced positivity preserving nonstaggered central scheme for open‐channel flows

In this paper, we construct and study an exactly well‐balanced positivity‐preserving nonstaggered central scheme for shallow water flows in open channels with irregular geometry and nonflat bottom topography. We introduce a novel discretization of the source term based on hydrostatic reconstruction to obtain the exactly well‐balanced property for the still water steady‐state solution even in the presence of wetting and drying transitions. The positivity‐preserving property of the cross‐sectional wet area is obtained by using a modified “draining" time‐step technique. The current scheme is also Riemann‐solver‐free. Several classical problems of open‐channel flows are used to test these properties. Numerical results confirm that the current scheme is robust, exactly well‐balanced and positivity‐preserving.