Joel C. W. Rogers

NUMERICAL SOLUTION OF A DIFFUSION CONSUMPTION PROBLEM WITH A FREE BOUNDARY

We consider the numerical solution of an implicit moving free boundary problem which arises in the study of diffusion and consumption of oxygen in tissue. A fixed domain numerical method is presented which is motivated by a theoretical formulation developed by Rogers. Our numerical method uses any convenient finite difference or finite element scheme which converges to the underlying partial differential equation. The frontal generation appears by way of a simple algebraic comparison operation involving truncation of the computed approximation. Higher space dimensions are treated with equal ease. Results of numerical experiments are presented. A convergence proof for the truncation method is given.

The Alternating Phase Truncation Method for Numerical Solution of a Stefan Problem

A numerical scheme for solving heat conduction problems involving a change of phase is presented. The numerical solution is obtained for heat flow in a two phase medium by using a method which treats each phase alternately, The resulting scheme avoids geometrical front tracking, and requires only simple algebraic operations. A maximum principle for the method and results of numerical experiments are given. An analytical version of the algorithm for a one dimensional one phase Stefan problem is shown to have an

A numerical algorithm for hydrodynamic free boundary problems

O(\Delta t \cdot \ln {{1}/{\Delta t}})^{{1/2}}

Numerical Solution of Hydrodynamic Free Boundary Problems

rate of convergence. Numerical experiments indicate that this estimate is sharp.

Mine detection using variational methods for image enhancement and feature extraction

A generalized formulation of inviscid incompressible hydrodynamics as a system of conservation laws subject to a one-sided density constraint is used as the basis of a numerical algorithm for a variety of hydrodynamic free surface problems. Benchmark calculations for colliding masses of fluid and for the motion of a spherically symmetric bubble are compared with theoretical predictions. Also shown are profiles calculated for an evolving underwater bubble near a wall. Energy dissipation is introduced as a measure of turbulence and is used in analyzing the numerical results. Convergence behavior of the numerical algorithm is discussed.

AN ALGORITHM FOR DIRECT SIMULATION OF LINEAR WAVE PROPAGATION IN IRREGULAR REGIONS

A generalized formulation of hydrodynamics as a system of conservation laws subject to a one-sided density constraint is used to solve a variety of hydrodynamic free surface problems. Consideration of the time derivative of the density constraint gives an alternative formulation in which an additional one-sided constraint on the divergence of the velocity appears. A corresponding numerical algorithm is presented, and benchmark calculations are compared with theoretical predictions. Also shown are profiles calculated for an evolving underwater bubble. Energy dissipation is introduced as a measure of turbulence and is used in analyzing the numerical results.

Numerical simulation of noise generated by wave breaking in a tank

A critical part of automatic classification algorithms is the extraction of features which distinguish targets from background noise and clutter. The focus of this paper is the use of variational methods for improving the classification of sea mines from both side-scan sonar and laser line-scan images. These methods are based on minimizing a functional of the image intensity. Examples include Total Variation Minimization (TVM) which is very effective for reducing the noise of an image without compromising its edge features, and Mumford-Shah segmentation, which in its simplest form, provides an optimal piecewise constant partition of the image. For the sonar side-scan images it is shown that a combination of these two variational methods, (first reducing the noise using TVM, then using segmentation) outperforms the use of either one individually for the extraction of minelike features. Multichannel segmentation based on a wavelet decomposition is also effectively used to declutter a sonar image. Finally, feature extraction and classification using segmentation is demonstrated on laser line-scan images of mines in a cluttered sea floor.

A hydro‐acoustic source model in calculating noise field generated by breaking waves

A numerical algorithm has been developed to simulate linear wave propagation in media containing irregular inhomogeneities, especially irregular voids in fluids. The computational domain is extended to include the regions occupied by the inhomogeneities through replacing the boundaries with properly chosen sources. The solution corresponding to Dirichlet boundary conditions on the inhomogeneities is presented. This algorithm can be used to calculate linear wave propagation in a fluid medium with multiple bubbles.

A numerical method for solving the problem

A coupled hydro‐acoustic source model in relating the physical parameters of wave breaking to the source quantities has been developed. The physical processes of wave formation and breaking are modeled using a generalized hydrodynamics formulation with the initial wave profile calculated by boundary integral method. Hydrodynamic parameters, such as pressure variations and air cavity shapes, etc., will be provided through the simulation. In the acoustic simulation, an algorithm has been developed in handling wave propagation in irregular regions, such as the bubbly liquid generated by wave breaking. To validate the modeling, an experiment on wave formation, propagation, and breaking is carried out in a wave tank. The waves are generated mechanically with a computer controlled vertically oscillating wedge. Favorable agreement is found upon comparing prediction and measurement. [Work supported by ONR.]

u_t - \Delta f (u) = 0

To develop a complete model for the breaking wave noise, it is necessary to relate the source quantities to the physical parameters of the wave‐breaking and noise‐generation processes. In this paper, the source structure of an individual breaking wave is simulated using a coupled hydro‐acoustic model, which incorporates the physical processes underlying the mechanisms of the generation of the noise. The physical processes of wave formation and breaking are modeled using a generalized hydrodynamics formulation, providing the hydrodynamic parameters, such as pressure variations and air cavity shapes, etc., for the acoustic calculation. In the acoustic simulation, an algorithm has been developed in handling wave propagation in irregular regions, such as the bubbly liquid generated by wave‐breaking. For the noise field modeling, the locations and occurrence times for the individual breaking waves are specified as stochastic quantities using Poisson simulations and the total noise field is calculated as the su...