A Quantitative Look at the Overshoot Problem in Mantle Convection Simulation Details Meeting 2013 Fall Meeting Section Study of Earth's Deep Interior Session State of the Art in Computational Geoscience I Posters [SWIRL_CM.CU] Identifier DI31A-2203 Authors Studley, E H*, Mathematics, University of California, Davis, Davis, CA, USA Heien, E M, Geology, University of California, Davis, Davis, CA, USA Kellogg, L H, Geology, University of California, Davis, Davis, CA, USA Puckett, E G, Mathematics, University of California, Davis, Davis, CA, USA Index Terms Numerical solutions [0560] General or miscellaneous [0599] General or miscellaneous [3299] Dynamics: convection currents, and mantle plumes [8121] Abstract In numerical models of mantle convection, overshoots of the computed temperature or compositional field will arise, for example, in a model of a rising plume or sinking subducted slab. The overshoot or undershoot will occur at the steep gradient of a scalar quantity such as temperature, and occurs in models in which advection dominates over diffusion. The overshoot and undershoot are caused when a second-order or higher method is used to model advection, causing an overestimation of fluxes along a steep gradient compared to lower-order method. Several methods have been developed for countering this effect, including streamline-upwind Petrov-Galerkin (SUPG), filtering techniques, and artificially increased diffusivity. As geodynamics research moves towards using numerical modeling to address multiscale physics, a small overshoot or undershoot can significantly alter quantities of interest including viscosity (which is exponentially temperature dependent) or the predicted location and quantity of melting. In our analysis, we find that the overshoot causes physically impossible oscillations in the calculated temperature solution, as well as incorrect plume formation and abnormal deformations in the pressure and velocity fields. We carry out a suite of models to characterize the overshoot-undershoot behavior of a finite element code in order to investigate the response to various methods for reducing this phenomenon. Cite as: Author(s) (2013), Title, Abstract DI31A-2203 presented at 2013 Fall Meeting, AGU, San Francisco, Calif., 9-13 Dec. --------------------------------------------------------------------------------================================================================================ Thursday, 14 December 2017 13:40 - 18:00 DI43A-1671 New Numerical Approaches for Modeling Thermochemical Convection in a Compositionally Stratified Fluid Elbridge Gerry Puckett1, Donald L Turcotte2, Ying He1, Harsha Venkata Lokavarapu3, Jonathan Robey3 and Louise H Kellogg2, (1)University of California Davis, Mathematics, Davis, CA, United States, (2)UC Davis, Department of Earth and Planetary Sciences, Davis, CA, United States, (3)University of California Davis, Davis, CA, United States Thursday, 14 December 2017 13:40 - 18:00 New Orleans Ernest N. Morial Convention Center - Poster Hall D-F 2015 T31E-07: Local Discontinuous Galerkin (LDG) Method for Advection of Active Compositional Fields with Discontinuous Boundaries: Demonstration and Comparison with Other Methods in the Mantle Convection Code ASPECT Flow in the Earth’s mantle is driven by thermo-chemical convection in which the properties and geochemical signatures of rocks vary depending on their origin and composition. For example, tectonic plates are composed of compositionally-distinct layers of crust, residual lithosphere and fertile mantle, while in the lower-most mantle there are large compositionally distinct “piles” with thinner lenses of different material. Therefore, tracking of active or passive fields with distinct compositional, geochemical or rheologic properties is important for incorporating physical realism into mantle convection simulations, and for investigating the long term mixing properties of the mantle. The difficulty in numerically advecting fields arises because they are non-diffusive and have sharp boundaries, and therefore require different methods than usually used for temperature. Previous methods for tracking fields include the marker-chain, tracer particle, and field-correction (e.g., the Lenardic Filter) methods: each of these has different advantages or disadvantages, trading off computational speed with accuracy in tracking feature boundaries. Here we present a method for modeling active fields in mantle dynamics simulations using a new solver implemented in the deal.II package that underlies the ASPECT software. The new solver for the advection-diffusion equation uses a Local Discontinuous Galerkin (LDG) algorithm, which combines features of both finite element and finite volume methods, and is particularly suitable for problems with a dominant first-order term and discontinuities. Furthermore, we have applied a post-processing technique to insure that the solution satisfies a global maximum/minimum. One potential drawback for the LDG method is that the total number of degrees of freedom is larger than the finite element method. To demonstrate the capabilities of this new method we present results for two benchmarks used previously: a falling cube with distinct buoyancy and viscosity, and a Rayleigh-Taylor instability of a compositionally buoyant layer. To evaluate the trade-offs in computational speed and solution accuracy we present results for these same benchmarks using the two field tracking methods available in ASPECT: active tracer particles and the entropy viscosity method. Authors Ying He University of California Davis Magali I Billen University of California Davis Elbridge Gerry Puckett University of California Davis -------------------------------------------------------------------------------- T22D-03: Discontinuous Galerkin (DG) Method for solving time dependent convection-diffusion type temperature equation : Demonstration and Comparison with Other Methods in the Mantle Convection Code ASPECT For a convection-dominated system, like convection in the Earth’s mantle, accurate modeling of the temperature field in terms of the interaction between convective and diffusive processes is one of the most common numerical challenges. In the geodynamics community using Finite Element Method (FEM) with artificial entropy viscosity is a popular approach to resolve this difficulty, but introduce numerical diffusion. The extra artificial viscosity added into the temperature system will not only oversmooth the temperature field where the convective process dominates, but also change the physical properties by increasing the local material conductivity, which will eventually change the local conservation of energy. Accurate modeling of temperature is especially important in the mantle, where material properties are strongly dependent on temperature. In subduction zones, for example, the rheology of the cold sinking slab depends nonlinearly on the temperature, and physical processes such as slab detachment, rollback, and melting all are sensitively dependent on temperature and rheology. Therefore methods that overly smooth the temperature may inaccurately represent the physical processes governing subduction, lithospheric instabilities, plume generation and other aspects of mantle convection. Here we present a method for modeling the temperature field in mantle dynamics simulations using a new solver implemented in the ASPECT software. The new solver for the temperature equation uses a Discontinuous Galerkin (DG) approach, which combines features of both finite element and finite volume methods, and is particularly suitable for problems satisfying the conservation law, and the solution has a large variation locally. Furthermore, we have applied a post-processing technique to insure that the solution satisfies a local discrete maximum principle in order to eliminate the overshoots and undershoots in the temperature locally. To demonstrate the capabilities of this new method we present benchmark results (e.g., falling sphere), and a simple subduction models with kinematic surface boundary condition. To evaluate the trade-offs in computational speed and solution accuracy we present results for the same benchmarks using the Finite Element entropy viscosity method available in ASPECT. Authors Ying He University of California Davis Elbridge Gerry Puckett University of California Davis Magali I Billen UC Davis Louise H Kellogg UC Davis Find Similar View Related Events Session Proposal: T22D State of the Art in Computational Geoscience I Section: Tectonophysics Day: Tuesday, 13 December 2016 ---------------------------------------------------------------------------- T22D-04: Implementing Flexible and Scalable Particle-in-Cell Methods for Massively Parallel Computations Particle-in-cell methods have a long history in modeling of mantle convection, lithospheric deformation and crustal dynamics. They are primarily used to track material information, the strain a material has undergone, the pressure-temperature history of a certain material, or the amount of volatiles or partial melt present in a region. However, their efficient parallel implementation - in particular combined with adaptive meshes - is complicated due to the complex communication and frequent reassignment of particles to cells. Consequently, many scientific software packages accomplish this efficiency by designing particle methods for a single purpose, like the advection of scalar properties that do not evolve over time (e.g., chemical heterogeneities). Design choices for particle advection, data storage, and parallel communication are then optimized for this single purpose, making the code rigid to changing requirements. Here, we present algorithms for a flexible, scalable and efficient particle-in-cell method for massively parallel finite-element codes with adaptively changing meshes. Using a modular plugin structure, we allow maximum flexibility of the generation of particles, the carried tracer properties, the advection and output algorithms, and the projection of properties to the finite-element mesh. We discuss the complexity of the these algorithms and present scaling tests ranging up to tens of thousands of cores and tens of billions of particles. We also discuss load-balancing strategies such as balanced repartitioning for particles in adaptive meshes, quantify sources of errors for the advection of particles, as well as how a proposed velocity correction can address the divergence of the velocity within a cell, and how higher-order finite elements can reduce the need for such a correction. Finally, we present whole mantle convection models as application cases, and compare our implementation to a modern advection-field approach.. We have implemented these algorithms in ASPECT (http://aspect.dealii.org), an open-source community code for mantle convection simulations. Authors Rene Gassmoeller Texas A&M University College Station Colorado State University Wolfgang Bangerth Colorado State University Texas A&M University College Station Elbridge Gerry Puckett University of California Davis Cedric Thieulot Utrecht University Eric M Heien University of California Davis