International Journal for Numerical Methods in Fluids

Pita, Claudio M.; Felicelli, Sergio D.

doi: 10.1002/fld.2006pmid: N/A

In this work, the immersed element‐free Galerkin method (IEFGM) is proposed for the solution of fluid–structure interaction (FSI) problems. In this technique, the FSI is represented as a volumetric force in the momentum equations. In IEFGM, a Lagrangian solid domain moves on top of an Eulerian fluid domain that spans over the entire computational region. The fluid domain is modeled using the finite element method and the solid domain is modeled using the element‐free Galerkin method. The continuity between the solid and fluid domains is satisfied by means of a local approximation, in the vicinity of the solid domain, of the velocity field and the FSI force. Such an approximation is achieved using the moving least‐squares technique. The method was applied to simulate the motion of a deformable disk moving in a viscous fluid due to the action of the gravitational force and the thermal convection of the fluid. An analysis of the main factors affecting the shape and trajectory of the solid body is presented. The method shows a distinct advantage for simulating FSI problems with highly deformable solids. Copyright © 2009 John Wiley & Sons, Ltd.

Liu, Qianlong; Vasilyev, Oleg V.

doi: 10.1002/fld.2011pmid: N/A

Nonlinear characteristic boundary conditions based on nonlinear multidimensional characteristics are proposed for 2‐ and 3‐D compressible Navier–Stokes equations with/without scalar transport equations. This approach is consistent with the flow physics and transport properties. Based on the theory of characteristics, which is a rigorous mathematical technique, multidimensional flows can be decomposed into acoustic, entropy, and vorticity waves. Nonreflecting boundary conditions are derived by setting corresponding characteristic variables of incoming waves to zero and by partially damping the source terms of the incoming acoustic waves. In order to obtain the resulting optimal damping coefficient, analysis is performed for problems of pure acoustic plane wave propagation and arbitrary flows. The proposed boundary conditions are tested on two benchmark problems: cylindrical acoustic wave propagation and the wake flow behind a cylinder with strong periodic vortex convected out of the computational domain. This new approach substantially minimizes the spurious wave reflections of pressure, density, temperature, and velocity as well as vorticity from the artificial boundaries, where strong multidimensional flow effects exist. The numerical simulations yield accurate results, confirm the optimal damping coefficient obtained from analysis, and verify that the method substantially improves the 1‐D characteristics‐based nonreflecting boundary conditions for complex multidimensional flows. Copyright © 2009 John Wiley & Sons, Ltd.

Li, C. W.; Zeng, C.

doi: 10.1002/fld.2012pmid: N/A

The passage of an extreme storm over an urban area can lead to the flooding of the streets if the rainfall intensity exceeds the design value and/or the drainage system is not functional. The study of flow distribution in street networks thus is important for the design of flood protection measures. The flow distribution is affected by the junction flow characteristics, inflow discharges and downstream water depths. To reduce the degree of empiricism, a 3D Reynolds‐averaged Navier–Stokes equations model has been implemented in this study to investigate the flow phenomena in a cross junction. The Spalart–Allmaras model is used for turbulence closure. The numerical model utilizes the split‐operator approach, in which the advection, diffusion and pressure propagations are solved separately. The numerical model predicts accurately the flow distribution in a channel crossing under different subcritical flow conditions, for which experimental data are available. Recirculation zones exist at both the downstream channels and the associated contraction coefficient varies linearly with the ratio of the discharges at the two inlets. Secondary currents are apparent for the flow with strong asymmetric outlet conditions. Under supercritical inflow conditions, the model reproduces the hydraulic jump and hydraulic drop phenomena and predicts accurately the relationship between the input power ratio and the outflow discharge ratio of the street crossing. Copyright © 2009 John Wiley & Sons, Ltd.

Alekseev, A. K.; Navon, I. M.

doi: 10.1002/fld.2015pmid: N/A

Criteria of optimality for sensors' location are addressed using an interpolation error transformed by especial adjoint problems. The considered criteria correspond to the analysis error in certain Hessian‐based metrics and to the error of some forecast aspect. Both criteria are obtained using adjoint problems that provide computation without the direct use of the Hessian. For a linear inverse heat conduction problem, these criteria are compared and demonstrated promising results when compared with a criterion based on the norm of the interpolation error of observation data. Approaches to sensor set modification using either redistribution of sensors' or refinement of the sensors grid (insertion of additional sensors) are also compared. Copyright © 2009 John Wiley & Sons, Ltd.

Richter, Thomas

doi: 10.1002/fld.2016pmid: N/A

In this work we develop a new framework for a posteriori error estimation and detection of anisotropies based on the dual‐weighted residual (DWR) method by Becker and Rannacher. The common approach for anisotropic mesh adaptation is to analyze the Hessian of the solution. Eigenvalues and eigenvectors indicate dominant directions and optimal stretching of elements. However, this approach is firmly linked to energy norm error estimation. Here, we extend the DWR method to anisotropic finite elements allowing for the direct estimation of directional errors with regard to given output functionals. The resulting meshes reflect anisotropic properties of both the solution and the functional. For the optimal measurement of the directional errors, the coarse meshes need some alignment with the dominant anisotropies. Numerical examples will demonstrate the efficiency of this method on various three‐dimensional problems including a well‐known Navier–Stokes benchmark. Copyright © 2009 John Wiley & Sons, Ltd.