Standard Ray-tracing Method Research Articles

Advances in numerical simulation of sonic boom in realistic atmospheres

Efficient and accurate numerical simulation of sonic boom is a key issue for both the design of low boom aircraft and the definition of a standard on supersonic overland flights. Atmospheric turbulence is known since the 1960s to significantly alter the ideal N-wave boom waveform. Such random fluctuations cannot be reproduced by the standard ray tracing method. Neither can it simulate the lateral boom beyond the geometrical carpet edge. There occur many non-geometrical features such as creeping waves, wave guiding or scattering. To progress in the direction of boom simulation beyond the geometrical approximation, we developed the so-called FLHOWARD3D software. For accuracy, it can handle 3D temperature, density or wind heterogeneities, atmospheric absorption, and nonlinear propagation effects. For efficiency, a one-way approximation is performed, neglecting the backscattered field. Nevertheless, the forward field satisfies an accurate dispersion relation, even in moving atmospheres. Involved physical effects are handled separately by optimized algorithms, combined by a second-order split-step approach. The resulting software is parallelized using the MPI paradigm. The performances of the software will be illustrated by two cases: boom scattering by turbulence, and lateral boom propagation in case of temperature inversion. This last case will be compared with flight test data.

GPU-accelerated iterative reconstruction from Compton scattered data using a matched pair of conic projector and backprojector

Background and ObjectiveIterative reconstruction from Compton scattered data is known to be computationally more challenging than that from conventional line-projection based emission data in that the gamma rays that undergo Compton scattering are modeled as conic projections rather than line projections. In conventional tomographic reconstruction, to parallelize the projection and backprojection operations using the graphics processing unit (GPU), approximated methods that use an unmatched pair of ray-tracing forward projector and voxel-driven backprojector have been widely used. In this work, we propose a new GPU-accelerated method for Compton camera reconstruction which is more accurate by using exactly matched pair of projector and backprojector. MethodsTo calculate conic forward projection, we first sample the cone surface into conic rays and accumulate the intersecting chord lengths of the conic rays passing through voxels using a fast ray-tracing method (RTM). For conic backprojection, to obtain the true adjoint of the conic forward projection, while retaining the computational efficiency of the GPU, we use a voxel-driven RTM which is essentially the same as the standard RTM used for the conic forward projector. ResultsOur simulation results show that, while the new method is about 3 times slower than the approximated method, it is still about 16 times faster than the CPU-based method without any loss of accuracy. ConclusionsThe net conclusion is that our proposed method is guaranteed to retain the reconstruction accuracy regardless of the number of iterations by providing a perfectly matched projector–backprojector pair, which makes iterative reconstruction methods for Compton imaging faster and more accurate.

Subgrid-scale model for radiative transfer in turbulent participating media

The simulation of turbulent flows of radiating gases, taking into account all turbulence length scales with an accurate radiation transport solver, is computationally prohibitive for high Reynolds or Rayleigh numbers. This is particularly the case when the small structures are not optically thin. We develop in this paper a radiative transfer subgrid model suitable for the coupling with direct numerical simulations of turbulent radiating fluid flows. Owing to the linearity of the Radiative Transfer Equation (RTE), the emission source term is spatially filtered to define large-scale and subgrid-scale radiation intensities. The large-scale or filtered intensity is computed with a standard ray tracing method on a coarse grid, and the subgrid intensity is obtained analytically (in Fourier space) from the Fourier transform of the subgrid emission source term. A huge saving of computational time is obtained in comparison with direct ray tracing applied on the fine mesh. Model accuracy is checked for three 3D fluctuating temperature fields. The first field is stochastically generated and allows us to discuss the effects of the filtering level and of the optical thicknesses of the whole medium, of the integral length scale, and of the cutoff wave length. The second and third cases correspond respectively to turbulent natural convection of humid air in a cubical box, and to the flow of hot combustion products inside a channel. In all cases, the achieved accuracy on radiative powers and wall fluxes is about a few percents.

Full-Wave Maxwell Simulations for Electron Cyclotron Resonance Heating

A new numerical scheme for electromagnetic wave tracing is presented in place of the standard ray-tracing method in studies of electron cyclotron resonance heating. The new method solves the full-wave Maxwell equations, and can take into account wave diffraction, mode conversion (or, cross-polarization scattering), and wave tunneling across an evanescent region between resonance and cutoff layers, in addition to estimating power absorption due to wave-particle resonances. The simulations of electromagnetic wave tunneling are demonstrated. The power absorption rate in electron cyclotron resonance heating is also compared with that by the ray-tracing method.

Determination of the influence zone for surface wave paths

SUMMARY An approximate description of the zone of influence around the propagation path for a surface wave is provided by investigating the Fresnel zones for the frequency range of interest. The influence zone about surface wave paths, over which surface waves are coherent in phase, is identified as approximately one-third of the width of the first Fresnel zone. A technique called Fresnel-area ray tracing (FRT) for surface waves has been used to estimate this region around the ray path for each frequency. The FRT technique is developed by combining two standard ray tracing methods, i.e. kinematic ray tracing (KRT) and dynamic ray tracing (DRT). To obtain the exact Fresnel area in a laterally heterogeneous structure would require the solution of a large number of KRT equations. In contrast, the FRT approach requires just a few ray tracing calculations. In the first step, the trajectory of the surface wave is computed by solving the KRT system for the phase-velocity distribution at the required frequency. In the next step, the behaviour of rays in the zone surrounding the KRT path is calculated by solving the DRT system twice; once from the source to the receiver and once more from the receiver to the source along the same trajectory. Finally, combining the solutions of these ray tracing systems using paraxial ray theory, the Fresnel area around a central ray can be estimated. Using FRT, stationary-phase fields can be constructed around a central ray path in a laterally heterogeneous structure. The influence zone around the ray path is then estimated from the stationary-phase function with simple assumptions concerning the perturbed wavefield. The estimate of the influence zone can be efficiently calculated in laterally heterogeneous structure by using the FRT technique, and allows an extension of current methods of surface wave analysis, which have commonly been based on geometrical ray theory and on the approximation of great-circle propagation. This approach allows the treatment of finite-width rays as well as deviations in propagation from the great circle induced by moderate lateral heterogeneity as revealed by recent tomography models. Such finite-width rays should be of major benefit in enhancing ray-based surface wave tomography.

TORBEAM, a beam tracing code for electron-cyclotron waves in tokamak plasmas

The beam tracing technique is used to describe the propagation and absorption of Gaussian wave beams with frequencies in the electron-cyclotron frequency range in a fusion plasma. Like in the standard ray tracing method, Maxwell's equations are reduced to a set of first-order ordinary differential equation. The technique employed here, however, allows for diffraction effects, neglected by the geometrical-optics procedure. The beam is specified in terms of the trajectory of the beam axis, the evolution of both the curvature of the wave front and the width of the field profile, as well as the absorption of the wave energy by the plasma. A Fortran code is presented, which solves the beam tracing equations in a tokamak geometry for arbitrary launching conditions and for both analytic and experimentally prescribed magnetic equilibria. Examples of wave propagation, power deposition and current profiles are computed and compared with ray tracing results.

EC beam tracing in fusion plasmas

The aim of the beam tracing technique is to include in the description of short-wavelength electromagnetic wave beams the effects of diffraction, which are neglected by the standard ray tracing method, but can play a significant role in focused or collimated wave beams. Beam tracing is, from a physical point of view, very close to other similar approaches, such as the parabolic equation and the complex eikonal description. In the beam tracing method, however, the problem is greatly simplified, since the full wave equation is reduced to a set of ordinary differential equations that describe the behaviour of the beam axis, the width of the beam and the curvature of the wave front. The propagation of an electromagnetic wave beam in a simplified (slab) geometry can be studied analytically. These calculations allow investigation of situations in which the role of diffraction becomes significant, and clarification of the basic mathematical features of the formalism. In order to solve the problem for realistic plasma geometries and arbitrary launching conditions for the wave beam, a numerical approach is necessary. A new code is presented, in which the beam tracing equations are integrated. Examples of absorption and current drive profiles are shown for RTO/RC ITER.

A NOTE ON LIGHT TRANSMISSION THROUGH AN EVOLVING SUSPENSION OF LIQUID DROPS

The intensity of light transmitted through an evolving suspension of two-dimensional deformable liquid drops in shear-driven or pressure-driven flow within a channel with parallel-sided walls is studied using a numerical method. The rays enter the suspension normal to upper wall, undergo reflections and refractions at the drop interfaces, and either return to the upper wall or leave from the lower wall. The motion and deformation of the drops are computed using a boundary integral method, and the optics is studied using a standard ray-tracing method. Evidence is presented that, in the case of shear-driven flow, a consistent correlation exists between the intensity of light transmitted through the channel, the geometry of the microstructure, and the global rheological properties of the emulsion. In the case of pressure-driven flow, a correlation between the transmitted intensity and the effective viscosity is also observed, but its features are not entirely consistent. These differences are attributed to t...