ХАРАКТЕРИСТИЧЕСКИЙ МЕТОД ДЛЯ РЕШЕНИЯ ЗАДАЧИ ФИЛЬТРАЦИИ
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При строительстве для улучшения свойств пористой породы в нее закачивается жидкий раствор укрепителя или водонепроницаемого наполнителя. Моделируется фильтрация суспензии, движущейся с переменной скоростью в пористой среде. Рассматривается одномерная задача фильтрации в однородной пористой среде с криволинейным фронтом концентраций взвешенных и осажденных частиц. Для численного решения задачи методом конечных разностей используется метод характеристик. Переход к характеристическим переменным позволяет выпрямить фронт и построить дискретную сетку с постоянным шагом. При вычислении решения по явной разностной схеме используются дополнительные точки, не совпадающие с узлами сетки. Приведено подробное описание алгоритма построения решения в узлах сетки и пример численного решения задачи.
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