New numerical approaches for modeling thermochemical convection in a compositionally stratified fluid

Seismic imaging of the mantle has revealed large and small scale heterogeneities in the lower mantle; specifically structures known as large low shear velocity provinces (LLSVP) below Africa and the South Pacific. Most interpretations propose that the heterogeneities are compositional in nature, differing in composition from the overlying mantle, an interpretation that would be consistent with chemical geodynamic models. Numerical modeling of persistent compositional interfaces presents challenges, even to state-of-the-art numerical methodology. For example, some numerical algorithms for advecting the compositional interface cannot maintain a sharp compositional boundary as the fluid migrates and distorts with time dependent fingering due to the numerical diffusion that has been added in order to maintain the upper and lower bounds on the composition variable and the stability of the advection method. In this work we present two new algorithms for maintaining a sharper computational boundary than the advection methods that are currently openly available to the computational mantle convection community; namely, a Discontinuous Galerkin method with a Bound Preserving limiter and a Volume-of-Fluid interface tracking algorithm. We compare these two new methods with two approaches commonly used for modeling the advection of two distinct, thermally driven, compositional fields in mantle convection problems; namely, an approach based on a high-order accurate finite element method advection algorithm that employs an artificial viscosity technique to maintain the upper and lower bounds on the composition variable as well as the stability of the advection algorithm and the advection of particles that carry a scalar quantity representing the location of each compositional field. All four of these algorithms are implemented in the open source FEM code ASPECT

SCIENTIFIC SOFTWARE ELEMENTS FOR MODELING PROCESSES IN THE EARTH'S MANTLE

Lightning Talk for the 2018 NSF SI2 PI Meetin

A Coupled Level Set and Volume of Fluid Method for computing 3d and axisymmetric Incompressible two-phase flows

We present a coupled level set and volume of fluid method (CLS) for computing 3d and axisymmetric incompressible two-phase flows. The (CLS) method combines some of the advantages of the level set approach (LS) with that of the volume of fluid approach (VOF). We do direct comparisons with computations using the level set method, volume of fluid method, and the boundary integral method. We also compare our computations to experimental results for a rising gas bubble in liquid. Our comparisons focus on ows in which surface tension forces and changes in topology are present in the flow

Final Report for DOE Grant DE-FG02-03ER25579; Development of High-Order Accurate Interface Tracking Algorithms and Improved Constitutive Models for Problems in Continuum Mechanics with Applications to Jetting

Much of the work conducted under the auspices of DE-FG02-03ER25579 was characterized by an exceptionally close collaboration with researchers at the Lawrence Berkeley National Laboratory (LBNL). For example, Andy Nonaka, one of Professor Miller's graduate students in the Department of Applied Science at U. C. Davis (UCD) wrote his PhD thesis in an area of interest to researchers in the Applied Numerical Algorithms Group (ANAG), which is a part of the National Energy Research Supercomputer Center (NERSC) at LBNL. Dr. Nonaka collaborated closely with these researchers and subsequently published the results of this collaboration jointly with them, one article in a peer reviewed journal article and one paper in the proceedings of a conference. Dr. Nonaka is now a research scientist in the Center for Computational Sciences and Engineering (CCSE), which is also part of the National Energy Research Supercomputer Center (NERSC) at LBNL. This collaboration with researchers at LBNL also included having one of Professor Puckett's graduate students in the Graduate Group in Applied Mathematics (GGAM) at UCD, Sarah Williams, spend the summer working with Dr. Ann Almgren, who is a staff scientist in CCSE. As a result of this visit Sarah decided work on a problem suggested by the head of CCSE, Dr. John Bell, for her PhD thesis. Having finished all of the coursework and examinations required for a PhD, Sarah stayed at LBNL to work on her thesis under the guidance of Dr. Bell. Sarah finished her PhD thesis in June of 2007. Writing a PhD thesis while working at one of the University of California (UC) managed DOE laboratories is long established tradition at UC and Professor Puckett has always encouraged his students to consider doing this. Another one of Professor Puckett's graduate students in the GGAM at UCD, Christopher Algieri, was partially supported with funds from DE-FG02-03ER25579 while he wrote his MS thesis in which he analyzed and extended work originally published by Dr. Phillip Colella, the head of ANAG, and some of his colleagues. Chris Algieri is now employed as a staff member in Dr. Bill Collins' Climate Science Department in the Earth Sciences Division at LBNL working with computational models of climate change. Finally, it should be noted that the work conducted by Professor Puckett and his students Sarah Williams and Chris Algieri and described in this final report for DOE grant # DE-FC02-03ER25579 is closely related to work performed by Professor Puckett and his students under the auspices of Professor Puckett's DOE SciDAC grant DE-FC02-01ER25473 An Algorithmic and Software Framework for Applied Partial Differential Equations: A DOE SciDAC Integrated Software Infrastructure Center (ISIC). Dr. Colella was the lead PI for this SciDAC grant, which was comprised of several research groups from DOE national laboratories and five university PI's from five different universities. In theory Professor Puckett tried to use funds from the SciDAC grant to support work directly involved in implementing algorithms developed by members of his research group at UCD as software that might be of use to Puckett's SciDAC CoPIs. (For example, see the work reported in Section 2.2.2 of this final report.) However, since there is considerable lead time spent developing such algorithms before they are ready to become `software' and research plans and goals change as the research progresses, Professor Puckett supported each member of his research group partially with funds from the SciDAC APDEC ISIC DE-FC02-01ER25473 and partially with funds from this DOE MICS grant DE-FC02-03ER25579. This has necessarily resulted in a significant overlap of project areas that were funded by both grants. In particular, both Sarah Williams and Chris Algieri were supported partially with funds from grant # DE-FG02-03ER25579, for which this is the final report, and in part with funds from Professor Puckett's DOE SciDAC grant # DE-FC02-01ER25473. For example, Sarah Williams received support from DE-FC02- 01ER25473 and DE-FC02-03ER25579, both while at UCD taking classes and writing her MS thesis and during the first year she was living in Berkeley and working at LBNL on her PhD thesis. In Chris Algieri's case he was at UCD during the entire time he received support from both grants. More specific details of their work are included in the report

A High-Order Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows

We present a numerical method for computing solutions of the incompressible Euler or Navier-Stokes equations when a principal feature of the flow is the presence of an interface between two fluids with different fluid properties. The method is based on a second-order projection method for variable density flows using an "approximate projection" formulation. The boundary between the fluids is tracked with a second-order, volume-of-fluid interface tracking algorithm. We present results for viscous Rayleigh-Taylor problems at early time with equal and unequal viscosities to demonstrate the convergence of the algorithm. We also present computational results for the Rayleigh-Taylor instability in air-helium and for bubbles and drops in an air-water system without interfacial tension to demonstrate the behavior of the algorithm on problems with larger density and viscosity contrasts. 1. Introduction Fluid flows with free surfaces or material interfaces occur in a large number of natural and ..