Aims. We consider the polarization arising from scattering in an envelope illuminated by a central anisotropic source. This work extends the theory introduced in a previous paper (Al-Malki et al. 1999) in which scattering polarization from a spherically symmetric envelope illuminated by an anisotropic point source was considered. Here we generalize to account for the more realistic expectation of a non-spherical envelope shape. Methods. Spherical harmonics are used to describe both the light source anisotropy and the envelope density distribution functions of the scattering particles. This framework demonstrates how the net resultant polarization arises from a superposition of three basic “shape” functions: the distribution of source illumination, the distribution of envelope scatterers, and the phase function for dipole scattering. Results. Specific expressions for the Stokes parameters and scattered flux are derived for the case of an ellipsoidal light source inside an ellipsoidal envelope, with principal axes that are generally not aligned. Two illustrative examples are considered: (a) axisymmetric mass loss from a rapidly rotating star, such as may apply to some Luminous Blue Variables, and (b) a Roche-lobe filling star in a binary system with a circumstellar envelope. Conclusions. As a general conclusion, the combination of source anisotropy with distorted scattering envelopes leads to more complex polarimetric behavior such that the source characteristics should be carefully considered when interpreting polarimetric data

The ultimate goal of this research is to develop the capability of direct numerical simulation of a flow containing numerous rigid finite size particles. In order to reach this goal, we have implemented the smoothed profile method (SPM) in the University of Iowa in-house solver, pELAFINT3D and overcame several challenges related to the method. This includes a proposed formulation for the interface thickness and many validations and comparisons with experimental data as well as with a second-order accurate sharp interface method. As one of the issues related to low-density particles is the instability, SPM has been improved by developing to a fully implicit scheme. Moreover, use of higher order integration formulation and implementation of Euler parameters have been shown to be helpful in stabilization of the calculations. To preserve the efficiency when the number of the particles increases, local mesh refinement is shown to be a very effective tool. A revised version of SPM that has only one projection step is proposed to improve the efficiency of the method. A comprehensive efficiency study is performed and it has been shown that the new method is less expensive in problems with high added mass effect when strongly coupled fluid-structure interaction schemes are used. Moreover, the code is massively parallelized using MPI and PETSc libraries. The parallelization includes I/O, operations leading to construction of the linear solver as well as the solver itself. Simulation of a particle laden flow involves particles collisions. Two novel collision models are suggested which are able to avoid particle overlapping for arbitrary shape particles. The methods are efficient as they are not involved with extra grid refinement related to implementing lubrication forces. The issue of handling continuously changing number of particles in a particle laden flow is solved by implementation of a linked list data structure for the particles. By studying a flow over a constricted region we showed that the platelets’ activation is more likely to happen for the particles that pass from the middle of the upper bump region because those particles will have longer exposure time to the high shear flow behind the bump. PDF contour of particles’ presence show the more concentrated presence of the particles near the bump. Moreover, the interaction of RBCs and platelets pushes the platelets toward the wall after the bottom wall.

An Automated Method for Hot-to-Cold Geometry Mapping.