TY - JOUR
T1 - An Exactly Mass Conserving and Pointwise Divergence Free Velocity Method
T2 - Application to Compositional Buoyancy Driven Flow Problems in Geodynamics
AU - Sime, Nathan
AU - Maljaars, Jakob M.
AU - Wilson, Cian R.
AU - van Keken, Peter E.
PY - 2021
Y1 - 2021
N2 - Tracer methods are widespread in computational geodynamics for modeling the advection of chemical data. However, they present certain numerical challenges, especially when used over long periods of simulation time. We address two of these in this work: the necessity for mass conservation of chemical composition fields and the need for the velocity field to be pointwise divergence free to avoid gaps in tracer coverage. We do this by implementing the hybrid discontinuous Galerkin (HDG) finite element (FE) method combined with a mass conserving constrained projection of the tracer data. To demonstrate the efficacy of this system, we compare it to other common FE formulations of the Stokes system and projections of the chemical composition. We provide a reference of the numerical properties and error convergence rates which should be observed by using these various discretization schemes. This serves as a tool for verification of existing or new implementations. We summarize these data in a reproduction of a published Rayleigh-Taylor instability benchmark, demonstrating the importance of careful choices of appropriate and compatible discretization methods for all aspects of geodynamics simulations.
AB - Tracer methods are widespread in computational geodynamics for modeling the advection of chemical data. However, they present certain numerical challenges, especially when used over long periods of simulation time. We address two of these in this work: the necessity for mass conservation of chemical composition fields and the need for the velocity field to be pointwise divergence free to avoid gaps in tracer coverage. We do this by implementing the hybrid discontinuous Galerkin (HDG) finite element (FE) method combined with a mass conserving constrained projection of the tracer data. To demonstrate the efficacy of this system, we compare it to other common FE formulations of the Stokes system and projections of the chemical composition. We provide a reference of the numerical properties and error convergence rates which should be observed by using these various discretization schemes. This serves as a tool for verification of existing or new implementations. We summarize these data in a reproduction of a published Rayleigh-Taylor instability benchmark, demonstrating the importance of careful choices of appropriate and compatible discretization methods for all aspects of geodynamics simulations.
KW - buoyancy driven convection
KW - finite element analysis
KW - mantle convection
KW - tracer methods
UR - http://www.scopus.com/inward/record.url?scp=85103360819&partnerID=8YFLogxK
U2 - 10.1029/2020GC009349
DO - 10.1029/2020GC009349
M3 - Article
AN - SCOPUS:85103360819
SN - 1525-2027
VL - 22
JO - Geochemistry, Geophysics, Geosystems
JF - Geochemistry, Geophysics, Geosystems
IS - 4
M1 - e2020GC009349
ER -