Apr 20th, 1:00 PM - 4:00 PM
Numerical Methods for Thermal Convection with Applications to the Earth’s Mantle
Dr. Grady Wright
Thermal convection is a universal phenomenon in nature and has many geophysical applications such as cloud formation in the atmosphere, solar convection, and motion in the Earth’s mantle. In its simplest form, thermal convection consists of heating a layer of fluid from below, which makes the fluid “top heavy”. If the buoyancy force induced by this heating overcomes the viscous force of the fluid then instability occurs and convective motion of the fluid begins. This type of instability often produces interesting patterns as anyone who has seen a Lava LampTM knows. In this poster, we restrict our attention to a thermal convection model for the Earth’s mantle, which is commonly called mantle convection. We discuss two numerical methods that can be used for simulating mantle convection in a 2D rectangular box. The first is a finite-difference method based on classical secondorder finite differences. The second can also be classified as a finite difference method, but is based on radial basis function approximations and is the first known application of this technique to simulating mantle convection. We also compare and contrast the stability, accuracy, and efficiency of the two techniques.