Interaction of laser radiation with the material during production powders and fibers

Воздействие лазерного излучения на твердое тело приводит к изменению температурного поля обрабатываемого вещества. Характер нагрева, определяющийся скоростями изменения температуры, температурных градиентов, оказывается различным в зависимости от свойств обрабатываемого материала и условий обработки. Основными физическими параметрами процесса лазерной обработки твердых тел являются удельная мощность поглощенного лазерного потока 104–109 Вт/см2 и время взаимодействия металла с лучом 10–5–10–8 с. При взаимодействии подобных импульсов излучения с поверхностью происходит мгновенное взрывоподобное плавление части материала и перевод окружающего поверхность вещества в плазменное состояние. Последующее расширение плазмы сопровождается возникновением ударной волны с пиковым давлением 1–10 ГПа, которая действует на материал, и имеет место диспергирование металла. Решена математическая задача нагрева и плавления цилиндрической пластины нормально падающим на ее поверхность световым потоком лазерного излучения, описываемая системой уравнений теплопроводности в трех сечениях нагреваемой пластины, которые характеризуются временным фактором воздействия лазерного излучения на вещество: 1) 0 ≤ t ≤ tm; 2) t > tm; 3) tm tm; 3) tm < t ≤ th (here tm, th is the time moment corresponding to the beginning of the formation of the liquid phase and the end of the melting of the plate, respectively). The calculated dependences of changes in the surface temperature of metal alloys X18N10T, X15N60 during the action of a laser radiation pulse with a duration of τ=5 ms are presented. The presence of a phase transition associated with metal melting (an inflection in the curves) leads to a temporary decrease in the rate of temperature growth. The distribution of temperature fields causes a significant heterogeneity in the distribution of temperature over the thickness of materials, which reaches 2000 °C or more depending on the thickness of the metal and the conditions of exposure. The temperature curves of the surface heating repeat the shape of the pulse, and the temperature of the rest of the metal has a nonlinear tendency to increase with the output to the asymptote. It is established that the process of explosive metal sputtering requires heating the volume of the material above the melting point at a thickness of 300–350 microns and an impact energy of 7–8 J. Reducing the level of energy impact to 5–6 J and increasing the thickness of the workpiece more than 500 microns does not provide the distribution of temperature fields required for the implementation of the spraying process

Earthquake Rupture Dynamics using Adaptive Mesh Refinement and High-Order Accurate Numerical Methods

Our goal is to develop scalable and adaptive (spatial and temporal) numerical methods for coupled, multiphysics problems using high-order accurate numerical methods. To do so, we are developing an opensource, parallel library known as bfam (available at http://bfam.in). The first application to be developed on top of bfam is an earthquake rupture dynamics solver using high-order discontinuous Galerkin methods and summation-by-parts finite difference methods. In earthquake rupture dynamics, wave propagation in the Earth's crust is coupled to frictional sliding on fault interfaces. This coupling is two-way, required the simultaneous simulation of both processes. The use of laboratory-measured friction parameters requires nearfault resolution that is 4-5 orders of magnitude higher than that needed to resolve the frequencies of interest in the volume. This, along with earlier simulations using a low-order, finite volume based adaptive mesh refinement framework, suggest that adaptive mesh refinement is ideally suited for this problem. The use of high-order methods is motivated by the high level of resolution required off the fault in earlier the low-order finite volume simulations; we believe this need for resolution is a result of the excessive numerical dissipation of low-order methods. In bfam spatial adaptivity is handled using the p4est library and temporal adaptivity will be accomplished through local time stepping. In this presentation we will present the guiding principles behind the library as well as verification of code against the Southern California Earthquake Center dynamic rupture code validation test problems

Linear and Nonlinear Boundary Conditions for Wave Propagation Problems

We discuss linear and nonlinear boundary conditions for wave propagation problems. The concepts of well-posedness and stability are discussed by considering a specific example of a boundary condition occurring in the modeling of earthquakes. That boundary condition can be formulated in a linear and nonlinear way and implemented in a characteristic and non-characteristic way. These differences are discussed and the implications and difficulties are pointed out. Numerical simulations that illustrate the theoretical discussion are presented together with an application that show that the methodology can be used for practical problems