Nonlinear localized dissipative structures for long-time solution of wave equation

In this dissertation, a new numerical method, Wave Confinement (WC), is developed to efficiently solve the linear wave equation. This is similar to the originally developed Vorticity Confinement method for fluid mechanics problems. It involves modification of the discrete wave equation by adding an extra nonlinear term that can accurately propagate the pulses for long distances without numerical dispersion/diffusion. These pulses are propagated as stable codimension-one surfaces and do not suffer phase shift or amplitude exchange in spite of nonlinearity. The pulses remain thin unlike conventional higher order numerical schemes, which only converge as N (number of grid cells across the pulse) becomes large. The additional term does not interfere with conservation of the important integral quantities such as total amplitude, centroid. Also, properties like varying index of refraction, diffraction, multiple reflections are included and tested.The generated short pulses can be best described as solitary waves, which can recover the shape after a collision due to nondestructive interaction between the pulses. Within the pulse, the dissipative effects due to the numerical errors are balanced with those of nonlinearity and the pulse will its their original form and speed even after many collisions. The pulse is also used as a carrier wave to propagate other properties such as direction. Wave equation solutions in the high frequency approximation can be generated using the carrier wave approach. WC, together with Keller\u27s Approximation is then used to capture diffraction effects from a straight edge. Scattering over complex bodies can be modeled with no use of complicated adaptive grid generation schemes around the bodies. The confinement term smoothens the boundary and prevents stair casing effects but the boundary remains thin.Validation studies have been performed for a number of real flow models and compared to the exact solutions. It is observed that the solutions match quite well with the exact solution. A new approximation for long range propagation of high frequency waves, the Local Parabolic Method , is introduced. There is a wide range of applications such as radio wave propagation, cell phone communications, target detection, etc. This approximation has a number of advantages over the existing paraxial approximation used to simulate radio wave propagation

Sound Diffraction Modeling of Rotorcraft Noise Around Terrain

A new computational technique, Wave Confinement (WC), is extended here to account for sound diffraction around arbitrary terrain. While diffraction around elementary scattering objects, such as a knife edge, single slit, disc, sphere, etc. has been studied for several decades, realistic environments still pose significant problems. This new technique is first validated against Sommerfeld's classical problem of diffraction due to a knife edge. This is followed by comparisons with diffraction over three-dimensional smooth obstacles, such as a disc and Gaussian hill. Finally, comparisons with flight test acoustics data measured behind a hill are also shown. Comparison between experiment and Wave Confinement prediction demonstrates that a Poisson spot occurred behind the isolated hill, resulting in significantly increased sound intensity near the center of the shadowed region

Computation of Helicopter Flow with Sand Pick-up

The computations of flow over an entire helicopter configuration, including main rotor and tail rotor, are performed on a uniform Cartesian grid. The rotor blades are represented by very efficient lifting lines using a simple momentum source representation together with the Flow Analysis Vorticity-Confinement-based flow solver. A particulate convection model, used to accommodate particles with mass and drag, and an entrainment module, capable of modeling different entrainment phenomena related to sand, snow, and other particulates are used for the computation. Visualization of the vorticity magnitude using advanced rendering is seen to be a very effective way to represent the flow field. The rendering using the package “Mental Ray” from Mental Images is seen to be a very effective, efficient means to visualize the flows in a realistic manner, and at a computational cost comparable to the actual, very efficient, flow computation. SAGE operates on uniform, coarse Cartesian grids. As a result, the flow solver algorithm does not require computations of grid metrics. The use of uniform Cartesian grids allows FFT-based Poisson solvers to be used, which is the most efficient approach known. Since most of the computational time is spent in the Poisson solution, the SAGE implementation is very efficient. In addition, the implementation accommodates the use of multiple embedded Cartesian meshes. Flows over complex configurations are computed by immersing the surface description of the configuration in the Cartesian. The ability to immerse solid surfaces within the Cartesian grid is of critical importance to this study. This represents a very simple, economical way to treat complex bodies since it does not require body conforming or adaptive grid generation and can use a fast Cartesian grid set-up and flow solver. Different helicopter and rotor configurations can be rapidly implemented without the time-consuming and tedious grid generation efforts required by other approaches.Accurate prediction of rotorcraft flow fields for brownout, computed using an incompressible flow solver SAGE with Vorticity Confinement, is demonstrated in our fluid dynamics video. The main problem addressed here is the simulation of effects of particulate pick-up during rotorcraft landing maneuvers, which can lead to very dangerous conditions, such as loss of visibility. This technical problem requires rapid, accurate prediction of rotorcraft flow fields in ground effect, including particulate pickup and transport, and its effects on pilot visibility (such as brownout from sand). Solution of this problem will give engineers a simulation tool with which they can develop landing descent trajectories and pilot training techniques that minimize these problems

Computation of Helicopter Flow with Sand Pick-up

The computations of flow over an entire helicopter configuration, including main rotor and tail rotor, are performed on a uniform Cartesian grid. The rotor blades are represented by very efficient lifting lines using a simple momentum source representation together with the Flow Analysis Vorticity-Confinement-based flow solver. A particulate convection model, used to accommodate particles with mass and drag, and an entrainment module, capable of modeling different entrainment phenomena related to sand, snow, and other particulates are used for the computation. Visualization of the vorticity magnitude using advanced rendering is seen to be a very effective way to represent the flow field. The rendering using the package “Mental Ray” from Mental Images is seen to be a very effective, efficient means to visualize the flows in a realistic manner, and at a computational cost comparable to the actual, very efficient, flow computation. SAGE operates on uniform, coarse Cartesian grids. As a result, the flow solver algorithm does not require computations of grid metrics. The use of uniform Cartesian grids allows FFT-based Poisson solvers to be used, which is the most efficient approach known. Since most of the computational time is spent in the Poisson solution, the SAGE implementation is very efficient. In addition, the implementation accommodates the use of multiple embedded Cartesian meshes. Flows over complex configurations are computed by immersing the surface description of the configuration in the Cartesian. The ability to immerse solid surfaces within the Cartesian grid is of critical importance to this study. This represents a very simple, economical way to treat complex bodies since it does not require body conforming or adaptive grid generation and can use a fast Cartesian grid set-up and flow solver. Different helicopter and rotor configurations can be rapidly implemented without the time-consuming and tedious grid generation efforts required by other approaches.Accurate prediction of rotorcraft flow fields for brownout, computed using an incompressible flow solver SAGE with Vorticity Confinement, is demonstrated in our fluid dynamics video. The main problem addressed here is the simulation of effects of particulate pick-up during rotorcraft landing maneuvers, which can lead to very dangerous conditions, such as loss of visibility. This technical problem requires rapid, accurate prediction of rotorcraft flow fields in ground effect, including particulate pickup and transport, and its effects on pilot visibility (such as brownout from sand). Solution of this problem will give engineers a simulation tool with which they can develop landing descent trajectories and pilot training techniques that minimize these problems

Computation of Helicopter Flow with Sand Pick-up

The computations of flow over an entire helicopter configuration, including main rotor and tail rotor, are performed on a uniform Cartesian grid. The rotor blades are represented by very efficient lifting lines using a simple momentum source representation together with the Flow Analysis Vorticity-Confinement-based flow solver. A particulate convection model, used to accommodate particles with mass and drag, and an entrainment module, capable of modeling different entrainment phenomena related to sand, snow, and other particulates are used for the computation. Visualization of the vorticity magnitude using advanced rendering is seen to be a very effective way to represent the flow field. The rendering using the package “Mental Ray” from Mental Images is seen to be a very effective, efficient means to visualize the flows in a realistic manner, and at a computational cost comparable to the actual, very efficient, flow computation. SAGE operates on uniform, coarse Cartesian grids. As a result, the flow solver algorithm does not require computations of grid metrics. The use of uniform Cartesian grids allows FFT-based Poisson solvers to be used, which is the most efficient approach known. Since most of the computational time is spent in the Poisson solution, the SAGE implementation is very efficient. In addition, the implementation accommodates the use of multiple embedded Cartesian meshes. Flows over complex configurations are computed by immersing the surface description of the configuration in the Cartesian. The ability to immerse solid surfaces within the Cartesian grid is of critical importance to this study. This represents a very simple, economical way to treat complex bodies since it does not require body conforming or adaptive grid generation and can use a fast Cartesian grid set-up and flow solver. Different helicopter and rotor configurations can be rapidly implemented without the time-consuming and tedious grid generation efforts required by other approaches.Accurate prediction of rotorcraft flow fields for brownout, computed using an incompressible flow solver SAGE with Vorticity Confinement, is demonstrated in our fluid dynamics video. The main problem addressed here is the simulation of effects of particulate pick-up during rotorcraft landing maneuvers, which can lead to very dangerous conditions, such as loss of visibility. This technical problem requires rapid, accurate prediction of rotorcraft flow fields in ground effect, including particulate pickup and transport, and its effects on pilot visibility (such as brownout from sand). Solution of this problem will give engineers a simulation tool with which they can develop landing descent trajectories and pilot training techniques that minimize these problems