Формулы для двумерного моделирования методом FDTD с использованием граничных условий на основе PML


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Иван Мелешко
Моделирование-4
В работе F. Collino, C. Tsogka. Application of the PML absorbing layer model to the linear elastodynamic очень хорошо и подробно расписано использование поглощающих слоев на основе PML (Perfect Matched Layers) с разделенными координатами для моделирования методом FDTD. Но есть одна проблема: уравнения там даны в виде соотношений, и для практического применения нужно выразить из них вычисляемый параметр. Вроде бы дело не сложное. Но из-за их громоздкости и запутанности пропустить ошибку в каком-нибудь индексе очень легко. На поиски же ее можно потратить не один день. Есть неплохая реализация этого метода на фортране. Тем не менее, в виде, пригодном для переноса в программу, мне эти формулы не встречались. Думаю, что тем, кто будет самостоятельно реализовывать PML, они могут пригодиться.

Вариант для участков вне зоны PML (базовая схема Верье с разделением координат на продольную и поперечную составляющие):









Для участков в зоне PML:









Где коэффициенты PML определяются:




Где:
скорость продольной волны
желаемый коэффициент затухания
толщина PML слоя
координата точки относительно PML слоя

Запись опубликована в рубрике wave equation, моделирование с метками , . Добавьте в закладки постоянную ссылку.

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