HR: 17:45h
AN: T54B-08    [Abstracts]
TI: A new Remesh-Lagrange technique for advecting temperature that minimizes numerical diffusion
AU: Hasenclever, J
EM: Joerg.Hasenclever@zmaw.de
AF: Hamburg University, BundesStr. 55, Institute of Geophysics, Hamburg, 20146, Germany
AU: * Phipps Morgan, J
EM: jp369@cornell.edu
AF: Cornell, EAS,Snee Hall, Cornell, Ithaca, NY 14850, United States
AU: Shi, C
EM: cs387@cornell.edu
AF: Cornell, EAS,Snee Hall, Cornell, Ithaca, NY 14850, United States
AB: The proper treatment of heat-advection is a generally underappreciated problem within CFD, yet particularly critical for calculating physically sound erosion in plume-lithosphere interactions and temperature sensitive melting processes. Typically, Eulerian (fixed-mesh) codes have been preferred to solve for fluid flow and they are almost essential for finite-difference-based algorithms. Unfortunately, the Eulerian approach introduces numerical artifacts into the solution of the advection-diffusion heat transport problem that can only be suppressed by adding 'too-diffusive' artificial diffusion to the equations, as for example in the Smolarkiewicz formulation for heat advection. We have developed a 'Remesh-Lagrange' method using a partly deforming finite element mesh and find it to be significantly more accurate than our previous methods. In several test scenarios we show the large improvement in accuracy that can be obtained by using a Lagrangian approach for 10-30 time steps (depending upon the distortion of the finite elements in the deformed Lagrangian mesh) and then regridding to the initial mesh. When an element becomes too distorted the nodes connected to it become fixed and we switch from Lagrange to a Semi-Lagrange formulation for these nodes. Instead of the standard 'linear backward' Semi-Lagrange we are also experimenting with a more accurate interpolation scheme for an unstructured mesh that additionally includes the nodal derivatives of the temperature field when calculating the value at the Semi-Lagrange traceback point. The same bicubic interpolation method for an unstructured grid is used to remesh the 'too-distorted' Lagrange grid back to the initial undistorted mesh. We compare the Remesh-Lagrange technique against the following Eulerian methods in a series of 2-D numerical experiments advecting stripes and Gaussian peaks in steady circulating flow: linear back-interpolation Semi-Lagrange method; bicubic back-interpolation Semi-Lagrange method; SUPG; and the Smolarkiewicz (flux- limiting diffusion) method, which is arguably the 'best-in-practice' of the Eulerian finite-difference methods. We also compare these methods for a test-case of diapiric upwelling that is forced by a pure chemical (non-diffusive) buoyancy associated with tracer particles that are advected by the plume upwelling. In this case, we find that the Eulerian methods typically underpredict the temperature of the plume head by about 20C, while overheating a ~50km region outside the plume-stem by about 10C in comparison to the Remesh-Lagrange technique.
DE: 3225 Numerical approximations and analysis (4260)
DE: 8121 Dynamics: convection currents, and mantle plumes
DE: 8130 Heat generation and transport
DE: 8137 Hotspots, large igneous provinces, and flood basalt volcanism
SC: Tectonophysics [T]
MN: 2007 Fall Meeting