Modelling, Analysis, & Simulations of Free Boundary/Moving Interface Problems - Professor Zhilin Li
4:00pm - 5:00pm /
Thursday 17th November 2016
/ Venue: MATH-104, First Floor Mathematical Sciences Building
Type: Seminar /
Category: Research
- Samantha D'Arcy
- Admission: No Cost
Add this event to my calendar
Click on "Create a calendar file" and your browser will download a .ics file for this event.
Microsoft Outlook: Download the file, double-click it to open it in Outlook, then click on "Save & Close" to save it to your calendar. If that doesn't work go into Outlook, click on the File tab, then on Open & Export, then Open Calendar. Select your .ics file then click on "Save & Close".
Google Calendar: download the file, then go into your calendar. On the left where it says "Other calendars" click on the arrow icon and then click on Import calendar. Click on Browse and select the .ics file, then click on Import.
Apple Calendar: The file may open automatically with an option to save it to your calendar. If not, download the file, then you can either drag it to Calendar or import the file by going to File >Import > Import and choosing the .ics file.
EPSRC Liverpool Centre for Mathematics in Healthcare (LCMH) “Modeling, Analysis, & Simulations of Free Boundary/Moving Interface Problems” - Professor Zhilin Li
Free boundary/moving interface problems are challenging both theoretically and numerically. In this general talk, I will introduce some application examples and corresponding differential equations models. The applications include Stefan problems of unstable crystal growth; drop spreading, and multi-phase flows. Then I will give a brief review of numerical methods for solving those challenging problems, particularly Cartesian grid method such as Peskin's Immersed Boundary (IB) method, the Immersed Interface Method (IIM), Augmented IIM, and Immersed finite element method (IFEM) developed by myself.
Another major component in solving free boundary/moving interface problems is how to evolve the interface. In our approach, both the front tracking and the level set methods are used. The level set method is simple and robust and can handle topological changes for any dimensions. I am going to discuss some issues about how to combine the level set method with IIM to achieve high order accuracy.
Free boundary/moving interface problems are challenging both theoretically and numerically. In this general talk, I will introduce some application examples and corresponding differential equations models. The applications include Stefan problems of unstable crystal growth; drop spreading, and multi-phase flows. Then I will give a brief review of numerical methods for solving those challenging problems, particularly Cartesian grid method such as Peskin's Immersed Boundary (IB) method, the Immersed Interface Method (IIM), Augmented IIM, and Immersed finite element method (IFEM) developed by myself.
Another major component in solving free boundary/moving interface problems is how to evolve the interface. In our approach, both the front tracking and the level set methods are used. The level set method is simple and robust and can handle topological changes for any dimensions. I am going to discuss some issues about how to combine the level set method with IIM to achieve high order accuracy.