International Journal for Numerical Methods in Fluids

Sescu, Adrian; Hixon, Ray

doi: 10.1002/fld.3833pmid: N/A

The accuracy of boundary conditions for computational aeroacoustics is a well‐known challenge, due in part to the necessity of truncating the flow domain and replacing the analytical boundary conditions at infinity with numerical boundary conditions. In particular, the inflow boundary condition involving turbulent velocity or scalar fields is likely to introduce spurious waves into the domain, therefore degrading the flow behavior and deteriorating the physical acoustic waves. In this work, a method to generate low‐noise, divergence‐free, synthetic turbulence for inflow boundary conditions is proposed. It relies on the classical view of turbulence as a superposition of random eddies convected with the mean flow. Within the proposed model, the vector potential and the requirement that the individual eddies must satisfy the linearized momentum equations about the mean flow are used. The model is tested using isolated eddies convected through the inflow boundary and an experimental benchmark data for spatially decaying isotropic turbulence. Copyright © 2013 John Wiley & Sons, Ltd.

Anumolu, Lakshman; Trujillo, Mario F.

doi: 10.1002/fld.3834pmid: N/A

A hybrid scheme for reinitializing the level set function and its gradient within the frame work of the augmented level set method is presented. It is based on first dividing the domain into an interfacial region (i.e. nodes close to the interface) and its complement. Within the interfacial region, the level set and its gradient are updated explicitly through a modified version of Newton's method (Chopp, 2001, SIAM J. Sci. Comput. 23 230‐244) and is implemented here within the context of Hermite polynomials. In the region away from the interface, the solution pertains to a semi‐Lagrangian implementation of the reinitialization equations, which are solved based on Hermite polynomials and are time marched with a single step and a multipoint scheme. It is shown that for various exercises, the present method predicts the signed distance function and its gradient to 4th and 3rd order (in space), respectively with regards to the L1, L2, and L ∞  norms, provided the level set field is sufficiently smooth. A range of test cases are also considered from the literature, where the present method is compared with existing methods and shown to be generally more accurate. Moreover, the well‐known issue of volume loss due to reinitialization is addressed successfully with the current implementation, even for objects that are of the size of one grid cell, and whose local radius of curvature falls below the local grid size. For both time marching schemes, it is shown that the L2 and L ∞  errors decay to negligible levels, are smooth in space, and do not exhibit temporal oscillations. Finally the performance of the hybrid scheme is evaluated by applying it on various kinematic test cases. For solid body rotation problems (zero deformation flow field), the benefit stemming from hybrid reinitialization is marginal. When applied to kinematic cases involving severe deformation, such as the standard vortex flow, the reinitialization strategy helps maintain a smooth level set field, which prevents serious numerical errors from developing.Copyright © 2013 John Wiley & Sons, Ltd.

Reusken, Arnold; Zhang, Yuanjun

doi: 10.1002/fld.3835pmid: N/A

We consider the numerical simulation of a three‐dimensional two‐phase incompressible flow with a viscous interface. The simulation is based on a sharp interface Navier–Stokes model and the Boussinesq–Scriven constitutive law for the interface viscous stress tensor. In the recent paper [Soft Matter 7, 7797–7804, 2011], a model problem with a spherical droplet in a Stokes Poiseuille flow with a Boussinesq–Scriven law for the surface viscosity has been analyzed. In that paper, relations for the droplet migration velocity are derived. We relate the results obtained with our numerical solver for the two‐phase Navier–Stokes model to these theoretical relations. Copyright © 2013 John Wiley & Sons, Ltd.

Zhao, Xiukun; Chen, Yanli; Gao, Yanni; Yu, Changhua; Li, Yonghai

doi: 10.1002/fld.3838pmid: N/A

Nonequilibrium radiation diffusion problems are described by the coupled radiation diffusion and material conduction equations. Because of the highly nonlinear, strong discontinuous, and tightly coupled phenomena, solving this kind of problems is a challenge. We construct two finite volume element schemes for the equations. One of them is monotone on many kinds of meshes, which is proved theoretically and verified by numerical tests. The other one is hard to satisfy the monotonicity, but this defect can be corrected by different repair techniques. Numerical results show that these new methods are practical and efficient on distorted meshes.Copyright © 2013 John Wiley & Sons, Ltd.