A two‐grid fictitious domain method for direct simulation of flows involving non‐interacting particles of a very small sizeDechaume, A.; Finlay, W. H.; Minev, P. D.
doi: 10.1002/fld.2119pmid: N/A
The full resolution of flows involving particles whose scale is hundreds or thousands of times smaller than the size of the flow domain is a challenging problem. A naive approach would require a tremendous number of degrees of freedom in order to bridge the gap between the two spatial scales involved. The approach used in the present study employs two grids whose grid size fits the two different scales involved, one of them (the micro‐scale grid) being embedded into the other (the macro‐scale grid). Then resolving first the larger scale on the macro‐scale grid, we transfer the so obtained data to the boundary of the micro‐scale grid and solve the smaller size problem. Since the particle is moving throughout the macro‐scale domain, the micro‐scale grid is fixed at the centroid of the moving particle and therefore moves with it. In this study we combine such an approach with a fictitious domain formulation of the problem resulting in a very efficient algorithm that is also easy to implement in an existing CFD code. We validate the method against existing experimental data for a sedimenting sphere, as well as analytical results for motion of an inertia‐less ellipsoid in a shear flow. Finally, we apply the method to the flow of a high aspect ratio ellipsoid in a model of a human lung airway bifurcation. Copyright © 2009 John Wiley & Sons, Ltd.
3D tangentially injected swirling recirculating flow in a nozzle with a slotted‐tube—Effects of groove parametersGuo, Hui‐Fen; Chen, Zhi‐Yong; Yu, Chong‐Wen
doi: 10.1002/fld.2120pmid: N/A
A numerical prediction for 3D swirling recirculating flow in an air‐jet spinning nozzle with a slotted‐tube is carried out with the realizable k–ε turbulence model. The effects of the groove parameters on the flow and yarn properties are investigated. The simulation results show that some factors, such as reverse flow upstream of the injector, vortex breakdown downstream of the injector, corner recirculation zone (CRZ) behind the step and vortex ring in the groove caused by the groove geometric variation, are significantly related to fluid flow, and consequently to yarn properties. With increasing groove height, the length of the CRZ increases, while the initial vortex ring in the groove decreases and a same direction rotating vortex forms in the bottom of the groove. Similarly, as the groove width increases, the extent of both vortex breakdown in downstream of the injectors and the vortex ring in the groove increases slightly, whereas the CRZ lengths in stream‐wise direction decrease. Some factors, such as the negative tangential velocities, the size of the vortex rings in the grooves and the CRZ, are constant for nozzles with different groove lengths. Copyright © 2009 John Wiley & Sons, Ltd.
Examination for adjoint boundary conditions in initial water elevation estimation problemsKurahashi, T.
doi: 10.1002/fld.2127pmid: N/A
I present here a method of generating a distribution of initial water elevation by employing the adjoint equation and finite element methods. A shallow‐water equation is employed to simulate flow behavior. The adjoint equation method is utilized to obtain a distribution of initial water elevation for the observed water elevation. The finite element method, using the stabilized bubble function element, is used for spatial discretization, and the Crank–Nicolson method is used for temporal discretizations. In addition to a method for optimally assimilating water elevation, a method is presented for determining adjoint boundary conditions. An examination using the observation data including noise data is also carried out. Copyright © 2009 John Wiley & Sons, Ltd.
A two‐dimensional finite volume morphodynamic model on unstructured triangular gridsBenkhaldoun, Fayssal; Sahmim, Slah; Seaïd, Mohammed
doi: 10.1002/fld.2129pmid: N/A
We discuss the application of a finite volume method to morphodynamic models on unstructured triangular meshes. The model is based on coupling the shallow water equations for the hydrodynamics with a sediment transport equation for the morphodynamics. The finite volume method is formulated for the quasi‐steady approach and the coupled approach. In the first approach, the steady hydrodynamic state is calculated first and the corresponding water velocity is used in the sediment transport equation to be solved subsequently. The second approach solves the coupled hydrodynamics and sediment transport system within the same time step. The gradient fluxes are discretized using a modified Roe's scheme incorporating the sign of the Jacobian matrix in the morphodynamic system. A well‐balanced discretization is used for the treatment of source terms. We also describe an adaptive procedure in the finite volume method by monitoring the bed–load in the computational domain during its transport process. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bed gradients that may form in the approximate solution. Numerical results are shown for a test problem in the evolution of an initially hump‐shaped bed in a squared channel. For the considered morphodynamical regimes, the obtained results point out that the coupled approach performs better than the quasi‐steady approach only when the bed–load rapidly interacts with the hydrodynamics. Copyright © 2009 John Wiley & Sons, Ltd.
On the development of a triple‐preserving Maxwell's equations solver in non‐staggered gridsSheu, Tony W. H.; Hung, Y. W.; Tsai, M. H.; Chiu, P. H.; Li, J. H.
doi: 10.1002/fld.2142pmid: N/A
We present in this paper a finite difference solver for Maxwell's equations in non‐staggered grids. The scheme formulated in time domain theoretically preserves the properties of zero‐divergence, symplecticity, and dispersion relation. The mathematically inherent Hamiltonian can be also retained all the time. Moreover, both spatial and temporal terms are approximated to yield the equal fourth‐order spatial and temporal accuracies. Through the computational exercises, modified equation analysis and Fourier analysis, it can be clearly demonstrated that the proposed triple‐preserving solver is computationally accurate and efficient for use to predict the Maxwell's solutions. Copyright © 2009 John Wiley & Sons, Ltd.
On accuracy and efficiency of constrained reinitializationHartmann, D.; Meinke, M.; Schröder, W.
doi: 10.1002/fld.2135pmid: N/A
The reinitialization, which is required to regularize the level set function, can be computationally expensive and hence is a determining factor for the overall efficiency of a level set method. However, it often has a significantly adverse impact on the accuracy of the level set solution. This short note is meant to shed light on the efficiency and accuracy issues of the reinitialization process. Using just one clearly defined level set propagation test case with an analytical solution the solutions obtained using a recently proposed efficient lower‐order constrained reinitialization (CR) scheme and standard low‐ and high‐order reinitialization schemes are juxtaposed to evidence the superiority of the novel CR formulation. It is shown that maintaining the location of the zero level set during the reinitialization is crucial for the accuracy and that the displacement caused by standard high‐order reinitialization schemes clearly outweighs the benefit of the high‐order smoothing of the level set function. Finally, results of a three‐dimensional problem are concisely reported to demonstrate the general applicability of the CR scheme. Copyright © 2009 John Wiley & Sons, Ltd.