Abstract. Modelling the pressure in the Earth's interior is a common problem in Earth sciences. In this study we propose a method based on the conservation of the momentum of a fluid by using a hydrostatic scenario or a uniformly moving fluid to approximate the pressure. This results in a partial differential equation (PDE) that can be solved using classical numerical methods. In hydrostatic cases, the computed pressure is the lithostatic pressure. In non-hydrostatic cases, we show that this PDE-based approach better approximates the total pressure than the classical 1D depth-integrated approach. To illustrate the performance of this PDE-based formulation we present several hydrostatic and non-hydrostatic 2D models in which we compute the lithostatic pressure or an approximation of the total pressure, respectively. Moreover, we also present a 3D rift model that uses that approximated pressure as a time-dependent boundary condition to simulate far-field normal stresses. 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 compare the result of this numerical model with a traditional rift model employing free-slip boundary conditions to demonstrate the first-order implications of considering “open” boundary conditions in 3D thermo-mechanical rift models.
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Development of a thermo-pressure acoustic model and its application in modeling three-dimensional acoustofluidic systems
Theoretical modeling of acoustofluidic systems faces extreme challenges as the thickness of the thermoviscous boundary layer is very small compared to the microscale fluid dimensions. The classical pressure acoustic model overcomes these difficulties and is extensively used in simulating three-dimensional (3D) or large two-dimensional (2D) acoustofluidic systems. However, this model cannot be applied to thermoviscous acoustofluidics, as it does not consider energy conservation. Modeling thermoviscous acoustofluidic systems is, therefore, difficult and restricted to small 2D systems only. Here, we have developed a thermo-pressure acoustic model that can effectively simulate thermoviscous acoustofluidic systems. The model has been validated with the full model by performing numerical simulations for a small 2D acoustofluidic system for which capturing the acoustic boundary layer effect is feasible using the full model. After successful validation, we demonstrate that the thermo-pressure acoustic model can also be applied to studying 3D acoustofluidic systems.
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- Award ID(s):
- 2108795
- PAR ID:
- 10414778
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 35
- Issue:
- 3
- ISSN:
- 1070-6631
- Page Range / eLocation ID:
- 036115
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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