A dissipative finite element model for free surface flow

In this paper, we develop a new computational framework to investigate the sloshing free surface flow of Newtonian and non-Newtonian fluids in the rectangular tanks. We simulate the flow via a two-phase model and employ the fixed unstructured mesh in the computation to avoid the mesh distortion and reconstruction. As for the solution of Navier–Stokes equation, we utilize the SUPG finite element method based on the splitting scheme. The same order interpolation functions are then used for velocity and pressure. Moreover, the moving interface is captured via the concise level set method. We take advantage of the implicit discontinuous Galerkin method to handle the solution of level set and its reinitialization equations. A mass correction technique is also added to ensure the mass conservation property. The dam break-free surface flow is simulated firstly to demonstrate the validity of our mathematical model. In addition, the sloshing Newtonian fluid in the tank with flat and rough bottoms is considered to illustrate the feasibility and robustness of our computational scheme. Finally, the development of free surface for non-Newtonian fluid is also studied in the two tanks, and the influence of power-law index on the sloshing fluid flow is analyzed.

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A one-dimensional line element model for transient free surface flow in porous media

Applied Mathematics and Computation ◽

10.1016/j.amc.2020.125747 ◽

2021 ◽

Vol 392 ◽

pp. 125747 ◽

Cited By ~ 1

Author(s):

Zuyang Ye ◽

Qingli Fan ◽

Shibing Huang ◽

Aiping Cheng

Keyword(s):

Porous Media ◽

Free Surface ◽

Line Element ◽

Free Surface Flow ◽

Element Model ◽

Surface Flow ◽

Flow In Porous Media ◽

One Dimensional

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The response of a glacier to a surface disturbance: a case study on Vatnajökull ice cap, Iceland

Annals of Glaciology ◽

10.3189/172756400781819914 ◽

2000 ◽

Vol 31 ◽

pp. 104-110 ◽

Cited By ~ 25

Author(s):

G. Aðalgeirsdóttir ◽

G. H. Gudmundsson ◽

H. Björnsson

Keyword(s):

Finite Element ◽

Finite Element Model ◽

Measurement Errors ◽

Element Model ◽

Horizontal Stress ◽

Surface Flow ◽

Repeated Measurements ◽

Ice Cap ◽

Elevation Changes ◽

Flow Velocities

AbstractIn the course of a tremendous outburst flood (jökulhlaup) following the subglacial eruption in Vatnajökull, Iceland, in October 1996, a depression in the surface of the ice cap was created as a result of ice melting from the walls of a subglacial tunnel. The surface depression was initially approximately 6 km long, 800 m wide and 100 m deep. This ˚canyon" represents a significant perturbation in the geometry of the ice cap in this area where the total ice thickness is about 200–400 m. We present results of repeated measurements of flow velocities and elevation changes in the vicinity of the canyon made over a period of about 2 years. The measurements show a reduction in the depth of the canyon and a concomitant decrease in surface flow towards it over time. By calculating the transient evolution of idealized surface depressions using both analytical zeroth- and first-order theories, as well as the shallow-ice approximation (SIA) and a finite-element model incorporating all the terms of the momentum equations we demonstrate the importance of horizontal stress gradients at the spatial scale of this canyon. The transient evolution of the canyon is calculated with a two-dimensional time-dependent finite-element model with flow parameters (the parameters A and n of Glen’s flow law) that are tuned towards an optimal agreement with measured flow velocities. Although differences between measured and calculated velocities are comparable to measurement errors, the differences are not randomly distributed. The model is therefore not verified in detail. Nevertheless the model reproduces observed changes in the geometry over a 15 month time period reasonably well The model also reproduces changes in both velocities and geometry considerably better than an alternative model based on the SIA.

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