Abstract
Modelling the lithostatic pressure in the Earth's interior is a common problem in Earth sciences. In this study we propose to compute the lithostatic pressure from the conservation of momentum reduced to the hydrostatic particular case. It results a partial differential equation that can be solved using the classical numerical methods. To show the usefulness of solving a PDE to compute the lithostatic pressure we propose two 2D models, one with a deformed mesh and one with a radial gravity acceleration vector and a concentric density distribution. Moreover, we also present a 3D rift model using the lithostatic pressure as a boundary condition. This model shows a high non cylindricity resulting from the Neumann boundary condition that is accomodated by strike-slip shear zones. We compare the result of this numerical model with a simple free-slip boundary conditions model to demonstrate the first order implications of considering "open" boundary conditions in 3D thermo-mechanical models.
Highlights
In Earth sciences and geodynamic modelling, computing the lithostatic pressure can be essential
This model shows a high degree of non-cylindrical deformation resulting from the stress boundary condition that is accommodated by strike-slip shear zones
We propose an efficient, mesh and numerical method independent way to compute the lithostatic pressure for all scenarios 1-5 above by solving a partial differential equation (PDE) for a hydrostatic equilibrium fluid
Summary
In Earth sciences and geodynamic modelling, computing the lithostatic pressure can be essential. I Di i where ρi is the density at the centroid of the segment Di. For the case of a uniform mesh with cell edges aligned with the gravity vector, all the cell edges / vertices are located along straight lines which are parallel to the direction of gravity. Eq (2) can be evaluated by traversing along a column associated with a set of cells (or vertices) In this special case, the sub-division of the integral is naturally defined by mesh cells. When performing simulations in parallel where the mesh is distributed 50 across multiple MPI ranks, even for the case of a uniform mesh aligned with the gravity vector the column-wise integration approach is somewhat complicated. 60 applied to Earth sciences and geodynamics to show the usefulness of this approach
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