Morphology of lava domes inferred from numerical modeling

2020 ◽  
Author(s):  
Alik Ismail-Zadeh ◽  
Oleg Melnik ◽  
Igor Tsepelev
Keyword(s):  
Incompressible Fluid ◽  
Characteristic Time ◽  
Heat Conduction Equation ◽  
Continuity Equation ◽  
Lava Dome ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Two Component ◽  
Lava Viscosity

<p>Several types of lava dome morphology can be distinguished depending on the flow rate and the rheology of magma. At an endogenous regime, magma is embedded inside the dome and fresh magma is not extruded on the surface; vice versa, at an exogenous regime, a fresh lava is extruded, and a lava obelisk is of particular interest. Sometimes obelisks reach hundreds of meters in height before they collapse. We present models of magma extrusion on the surface and lava dome evolution to analyze morphology of the domes. For this aim, we consider a flow of a Newtonian and non-Newtonian viscous inhomogeneous incompressible fluid in the field of gravity. The flow is described by the Navier-Stokes equations, the continuity equation, the transport equation of a two-component incompressible fluid, the heat conduction equation, and the rheological law. The lava viscosity in our models depends on the crystals concentration, temperature, and the rate of shear deformation. We show that the morphology of the domes depends on the characteristic time of crystal growths in the magma and on the rate of magma extrusion. In this case, obelisks are formed at a small value of the characteristic time of growth of crystals and/or low extrusion rates. At high values of the characteristic time and high extrusion rates, magma spreads over the surface after an eruption.</p>

scholarly journals The inf-sup stability of the lowest order Taylor–Hood pair on affine anisotropic meshes

2019 ◽  
Vol 40 (4) ◽  
pp. 2377-2398
Author(s):  
Gabriel R Barrenechea ◽  
Andreas Wachtel
Keyword(s):  
Finite Element ◽  
Fluid Mechanics ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Sufficient Conditions ◽  
Navier Stokes ◽  
Element Solution ◽  
Navier Stokes Equations ◽  
Anisotropic Meshes ◽  
Theoretical Results

Abstract Uniform inf-sup conditions are of fundamental importance for the finite element solution of problems in incompressible fluid mechanics, such as the Stokes and Navier–Stokes equations. In this work we prove a uniform inf-sup condition for the lowest-order Taylor–Hood pairs $\mathbb{Q}_2\times \mathbb{Q}_1$ and $\mathbb{P}_2\times \mathbb{P}_1$ on a family of affine anisotropic meshes. These meshes may contain refined edge and corner patches. We identify necessary hypotheses for edge patches to allow uniform stability and sufficient conditions for corner patches. For the proof, we generalize Verfürth’s trick and recent results by some of the authors. Numerical evidence confirms the theoretical results.

scholarly journals Numerical Simulation of Micromixing of Particles and Fluids with Galloping Cylinder

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 580 ◽  
Author(s):  
Zahra Abdelmalek ◽  
Mohammad Yaghoub Abdollahzadeh Jamalabadi
Keyword(s):  
Continuity Equation ◽  
Stokes Equations ◽  
The Self ◽  
Moving Mesh ◽  
Navier Stokes ◽  
Parameter Study ◽  
Mems Devices ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Moving Cylinder

Micromixers are significant segments inside miniaturized scale biomedical frameworks. Numerical investigation of the effects of galloping cylinder characteristics inside a microchannel Newtonian, incompressible fluid in nonstationary condition is performed. Governing equations of the system include the continuity equation, and Navier–Stokes equations are solved within a moving mesh domain. The symmetry of laminar entering the channel is broken by the self-sustained motion of the cylinder. A parameter study on the amplitude and frequency of passive moving cylinder on the mixing of tiny particles in the fluid is performed. The results show a significant increase to the index of mixing uses of the galloping body in biomedical frameworks in the course of micro-electromechanical systems (MEMS) devices.

Time-dependent solutions of the Navier–Stokes equations for spatially-uniform velocity gradients

1994 ◽  
Vol 124 (1) ◽  
pp. 127-136 ◽  
Author(s):  
A. D. D. Craik
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Navier Stokes Equations ◽  
Temporal Behaviour ◽  
Uniform Velocity ◽  
Velocity Gradients

Classes of exact solutions of the Navier–Stokes equations for incompressible fluid flow are explored. These have spatially-uniform velocity gradients at each instant, but often display complex temporal behaviour. Particular illustrative cases are described and related to previously-known solutions.

scholarly journals Stability Analysis of Symmetrical Rotors Partially Filled with a Viscous Incompressible Fluid

2001 ◽  
Vol 7 (5) ◽  
pp. 301-310 ◽  
Author(s):  
Zhu Changsheng
Keyword(s):  
Stability Analysis ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Damping Ratio ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Navier Stokes Equations ◽  
Rotor Systems ◽  
The Stability

On the basis of the linearized fluid forces acting on the rotor obtained directly by using the two-dimensional Navier-Stokes equations, the stability of symmetrical rotors with a cylindrical chamber partially filled with a viscous incompressible fluid is investigated in this paper. The effects of the parameters of rotor system, such as external damping ratio, fluid fill ratio, Reynolds number and mass ratio, on the unstable regions are analyzed. It is shown that for the stability analysis of fluid filled rotor systems with external damping, the effect of the fluid viscosity on the stability should be considered. When the fluid viscosity is included, the adding external damping will make the system more stable and two unstable regions may exist even if rotors are isotropic in some casIs.

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