A nodally condensed SUPG formulation for free-surface computation of steady-state flows constrained by unilateral contact - Application to rolling

2018 ◽  
Author(s):  
Shitij Arora ◽  
Lionel Fourment
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Unilateral Contact ◽  
Supg Formulation

scholarly journals Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 505-515 ◽  
Author(s):  
D. C. Gakenheimer ◽  
J. Miklowitz
Keyword(s):  
Exact Solution ◽  
Free Surface ◽  
Steady State ◽  
Wave Front ◽  
Half Space ◽  
Displacement Field ◽  
Elastic Half Space ◽  
Point Load ◽  
Limit Case ◽  
Transient Waves

The propagation of transient waves in a homogeneous, isotropic, linearly elastic half space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are derived for the interior of the half space and for all load speeds. Wave-front expansions are obtained from the exact solution, in addition to results pertaining to the steady-state displacement field. The limit case of zero load speed is considered, yielding new results for Lamb’s point load problem.

scholarly journals Diagnostic and prognostic simulations with a full Stokes model accounting for superimposed ice of Midtre Lovénbreen, Svalbard

2009 ◽  
Vol 3 (2) ◽  
pp. 217-229 ◽  
Author(s):  
T. Zwinger ◽  
J. C. Moore
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Thermal State ◽  
Steady State Solution ◽  
Radar Data ◽  
Data Set ◽  
Surface Evolution ◽  
Steady State Model ◽  
Elevation Changes ◽  
Ground Penetrating

Abstract. We present steady state (diagnostic) and transient (prognostic) simulations of Midtre Lovénbreen, Svalbard performed with the thermo-mechanically coupled full-Stokes code Elmer. This glacier has an extensive data set of geophysical measurements available spanning several decades, that allow for constraints on model descriptions. Consistent with this data set, we included a simple model accounting for the formation of superimposed ice. Diagnostic results indicated that a dynamic adaptation of the free surface is necessary, to prevent non-physically high velocities in a region of under determined bedrock depths. Observations from ground penetrating radar of the basal thermal state agree very well with model predictions, while the dip angles of isochrones in radar data also match reasonably well with modelled isochrones, despite the numerical deficiencies of estimating ages with a steady state model. Prognostic runs for 53 years, using a constant accumulation/ablation pattern starting from the steady state solution obtained from the configuration of the 1977 DEM show that: 1 the unrealistic velocities in the under determined parts of the DEM quickly damp out; 2 the free surface evolution matches well measured elevation changes; 3 the retreat of the glacier under this scenario continues with the glacier tongue in a projection to 2030 being situated ≈500 m behind the position in 1977.

Ideal planar fluid flow over a submerged obstacle: Review and extension

2021 ◽  
Vol 63 ◽  
pp. 377-419
Author(s):  
Larry K. Forbes ◽  
Stephen J. Walters ◽  
Graeme C. Hocking
Keyword(s):  
Fluid Flow ◽  
Free Surface ◽  
Steady State ◽  
Gravity Waves ◽  
Classical Problem ◽  
Time Dependent ◽  
Time Dependent Behaviour ◽  
Critical Overview ◽  
Dependent Behaviour ◽  
Obstacle Height

A classical problem in free-surface hydrodynamics concerns flow in a channel, when an obstacle is placed on the bottom. Steady-state flows exist and may adopt one of three possible configurations, depending on the fluid speed and the obstacle height; perhaps the best known has an apparently uniform flow upstream of the obstacle, followed by a semiinfinite train of downstream gravity waves. When time-dependent behaviour is taken into account, it is found that conditions upstream of the obstacle are more complicated, however, and can include a train of upstream-advancing solitons. This paper gives a critical overview of these concepts, and also presents a new semianalytical spectral method for the numerical description of unsteady behaviour. doi:10.1017/S1446181121000341

How fault creep makes its way!

2020 ◽  
Author(s):  
Sohom Ray ◽  
Dmitry Garagash
Keyword(s):  
Free Surface ◽  
Steady State ◽  
High Stress ◽  
Slip Rate ◽  
Interfacial Strength ◽  
Elastic Half Space ◽  
Entire Length ◽  
Fault Creep ◽  
Dynamic Event ◽  
First Case

<p>We model mechanics of an aseismic fault creep propagation and conditions when it may lead to the initiation of seismic slip. We do so by considering fault bounding medium to be elastically deformable and fault's interfacial strength to be slip rate- and state-dependent characterized by the steady-state rate-weakening. The fault is considered to be initially locked: a state of slip when interfacial slip velocity is considerably low and arbitrarily less than the steady-state sliding rate for given uniformly distributed prestress.</p><p>We find solutions for creep penetration into the fault under geologically relevant loading scenarios (e.g., that of a plate-bounding strike-slip faulting driven by the slip at depth, or that of a rate-weakening patch of a fault loaded by a creep on an adjacent rate-strengthening part due to, e.g., anthropogenic fluid injection). In all the cases, the creep makes its way as a self-similar traveling front characterized by high stress owed to the direct effect; however, the remaining creep profile exhibits a near steady-state sliding. This may imply that a choice from a set of rules for the evolution of state variable—with identical linearizations about steady-state sliding—has no bearing on the creep penetration. Further, we find that the prestress, close to or far from steady-state sliding stress, controls the rate and manner of the creep penetration.</p><p>We study slip propagation from an imposed dislocation accrued at a constant rate at one end of a homogeneous fault with the other end either at (1) the free surface of an elastic half-space or (2) strictly locked (buried) in the elastic full space. In both scenarios, no slip instability takes place over aseismic creep propagation distances relatable to the usual elasto-frictional nucleation lengthscale (e.g. Rubin & Ampuero 2005). Instead, in the first case creep propagation leads to the nucleation of the first and all subsequent dynamic events of the emerging cycle at/near the free surface after the creep traversed the entire length of the fault. In the second case, the creep front traverses nearly the entire length of the fault, but, instead of nucleating a dynamic event, the front arrests at some distance from the buried fault end, followed by the continual accumulation of aseismic slip without ever nucleating a dynamic event. These results may be owed to the physical and geometrical invariance of the considered homogeneous fault and may signal the essential role of fault strength heterogeneity, either that of the normal stress and/or frictional properties (Ray & Viesca, 2017, 2019), in defining its seismogenic character, i.e. under which conditions and where on the fault the earthquake slip instability can take place. </p>

Weak Formulations with Upwind Shift for Calculation of Free Surface Corrections and Simulation of Steady-State Forming Problems

2014 ◽  
Vol 611-612 ◽  
pp. 1311-1318
Author(s):  
Lionel Fourment ◽  
Ugo Ripert
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Metal Forming ◽  
Wire Drawing ◽  
Computational Time ◽  
Steady Regime ◽  
Order Of Magnitude ◽  
Material Forming ◽  
Dramatic Shift ◽  
Simulation Time

For many material forming processes steady-state formulations allows reducing numerical simulation time by an order of magnitude with respect to more conventional approaches. In the presented approach, the steady regime is iteratively computed by a free surface algorithm that alternates computations of the metal forming flow over a known geometry and known contact surfaces, with computations of domain corrections to satisfy free and contact surface conditions. Several weak formulations of the second problem equations are investigated to get a robust algorithm suitable for parallel computations with unstructured meshes. Analytical problems show the necessity to introduce an upwind shift within these weak formulations. Contact inequations enforces this necessity by requiring a more dramatic shift. A robust and accurate algorithm is so obtained, which is successfully applied to 3D complex metal forming processes like rolling. In the wire drawing application, computational time is reduced by more than fifteen with respect to the incremental calculation of the steady-state.

Nonlinear free-surface flow due to an impulsively started submerged point sink

1998 ◽  
Vol 364 ◽  
pp. 325-347 ◽  
Author(s):  
MING XUE ◽  
DICK K. P. YUE
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Numerical Study ◽  
Free Surface Flow ◽  
Small Time ◽  
Surface Flow ◽  
Boundary Integral ◽  
Critical Regime ◽  
Gravitational Acceleration ◽  
Nonlinear Free Surface

The unsteady fully nonlinear free-surface flow due to an impulsively started submerged point sink is studied in the context of incompressible potential flow. For a fixed (initial) submergence h of the point sink in otherwise unbounded fluid, the problem is governed by a single non-dimensional physical parameter, the Froude number, [Fscr ]≡Q/4π(gh5)1/2, where Q is the (constant) volume flux rate and g the gravitational acceleration. We assume axisymmetry and perform a numerical study using a mixed-Eulerian–Lagrangian boundary-integral-equation scheme. We conduct systematic simulations varying the parameter [Fscr ] to obtain a complete quantification of the solution of the problem. Depending on [Fscr ], there are three distinct flow regimes: (i) [Fscr ]<[Fscr ]1≈0.1924 – a ‘sub-critical’ regime marked by a damped wave-like behaviour of the free surface which reaches an asymptotic steady state; (ii) [Fscr ]1<[Fscr ]<[Fscr ]2≈0.1930 – the ‘trans-critical’ regime characterized by a reversal of the downward motion of the free surface above the sink, eventually developing into a sharp upward jet; (iii) [Fscr ]>[Fscr ]2 – a ‘super-critical’ regime marked by the cusp-like collapse of the free surface towards the sink. Mechanisms behind such flow behaviour are discussed and hydrodynamic quantities such as pressure, power and force are obtained in each case. This investigation resolves the question of validity of a steady-state assumption for this problem and also shows that a small-time expansion may be inadequate for predicting the eventual behaviour of the flow.

scholarly journals On Filtration in a Rectangular Interchange with a particularly Unpermatable Vertical wall in the Evaporation

2021 ◽  
Vol 1 (1) ◽  
pp. 11-19
Author(s):  
E.N. Bireslavskii ◽  
L.M. Dudina
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Boundary Value Problem ◽  
Analytic Functions ◽  
Boundary Value ◽  
Vertical Wall ◽  
Hydrodynamic Analysis ◽  
Proposed Model ◽  
Efficiency And Productivity

We consider a plane steady-state filtration in a rectangular bridge with a partially impermeable vertical wall in the presence of evaporation from a free surface of groundwater. To study the effect of evaporation, a mixed multiparametric boundary-value problem of the theory of analytic functions is formulated and using the method of P. Y. Polubarinova-Kochina. Based on the proposed model, an algorithm is developed to calculate the dependence of efficiency and productivity of hydrodynamic analysis.

Measurement of Fluid Flow Thickness Within a Rotating Cone

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Digby D. Symons ◽  
Arnaud F. M. Bizard
Keyword(s):  
Fluid Flow ◽  
Free Surface ◽  
Steady State ◽  
Theoretical Model ◽  
Laminar Flow ◽  
Internal Surface ◽  
Vertical Axis ◽  
Experimental Measurements ◽  
Rotating Cone ◽  
Good Agreement

This paper reports experimental measurements of film thickness for continuous fluid flow on the internal surface of a cone rotating about a vertical axis. Measurements were obtained via an optical method based on photographing the displacement of a grid projected onto the surface of the flow within the cone. Results are compared to analytical theory for axisymmetric, steady state, free-surface laminar flow of a Newtonian fluid in a spinning cone. The theory assumes that the flow is thin but takes account of gravity. The theoretical model is found to be in good agreement with the experimental results.

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