A benchmark comparison for mantle convection codes

Abstract

We have carried out a comparison study for a set of benchmark problems which are relevant for convection in the Earth's mantle. The cases comprise steady isoviscous convection, variable viscosity convection and time-dependent convection with internal heating. We compare Nusselt numbers, velocity, temperature, heat-flow , topography and geoid data. Among the applied codes are finite-difference, finite-element and spectral methods. In a synthesis we give best estimates of the 'true' solutions and ranges of uncertainty. We recommend these data for the validation of convection codes in the future.

The effective viscosity of rocksalt: implementation of steady-state creep laws in numerical models of salt diapirism

“…We followed Christensen and Yuen (1984) in the implementation of the buoyancy forces and the advection of the markers, using a predictor-corrector method. Both finite element methods were tested against a variety of analytical models, and against published numerical models for Rayleigh-Taylor instabilities (e.g., Poliakov and Podladchikov, 1992) and showed good agreement, The method using the non-conforming element has also been extensively tested for mantle convection problems and it compares well with Hansen's implementation in the European mantle convection benchmark (Blankenbach et al, 1989). The codes were checked against a non-Newtonian benchmark published in Malevsky and Yuen (19921, that made a comparison between the independent spline methods of both Christensen and Malevsky, and the primitive variable method published in Van Keken et al (1992) and Van den Berg et al (1993).…”

Verification of cardiac tissue electrophysiology simulators using an N -version benchmark

“…Some studies have aimed to combine the two strategies by proposing a benchmark problem and simulating it on multiple codes at the same time. The Earth mantle simulation community has applied this approach to develop a series of benchmark problems and at the same time compared 12 simulation codes [25]. This strategy has the added benefits that it both compares many current codes and demonstrates that the defined benchmark is reproducible and unambiguously defined.…”

Mantle plumes and flood basalts: Enhanced melting from plume ascent and an eclogite component

“…We ran the simulations using the finite difference, multigrid program CONMG, which has been successfully compared with published benchmarks [Blankenbach et al, 1989] and unpublished finite element solutions [Davies, 1995] …”