NON-CARTESIAN, TOPOGRAPHY-BASED AVALANCHE EQUATIONS AND APPROXIMATIONS OF GRAVITY DRIVEN FLOWS OF IDEAL AND VISCOUS FLUIDS

2009 ◽  
Vol 19 (01) ◽  
pp. 127-171 ◽  
Author(s):  
I. LUCA ◽  
Y. C. TAI ◽  
C. Y. KUO
Keyword(s):  
Thin Layer ◽  
Three Dimensional ◽  
Physical Modelling ◽  
Viscous Fluids ◽  
Curvilinear Coordinates ◽  
Governing Equations ◽  
Tensor Fields ◽  
Full Generality ◽  
Gravity Driven ◽  
Arbitrary Topography

When dealing with geophysical flows across three-dimensional topography or other thin layer flows, for the physical modelling and for computational reasons, it is more convenient to use curvilinear coordinates adapted to the basal solid surface, instead of the Cartesian coordinates. Using such curvilinear coordinates, e.g. introduced by Bouchut and Westdickenberg,3 and the corresponding contravariant components of vector and tensor fields, we derive in full generality the governing equations for the avalanche mass. These are next used to deduce (i) the thin layer equations for arbitrary topography, when the flowing mass is an ideal fluid, and (ii) the thin layer equations corresponding to arbitrary topography and to a viscous fluid that experiences bottom friction, modelled by a viscous sliding law.

scholarly journals The intrinsic theory of linearly elastic plates

2018 ◽  
Vol 24 (4) ◽  
pp. 1182-1203 ◽  
Author(s):  
Philippe G. Ciarlet ◽  
Cristinel Mardare
Keyword(s):  
Boundary Condition ◽  
Elastic Plate ◽  
Tensor Field ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Middle Surface ◽  
Curvilinear Coordinates ◽  
Constant Thickness ◽  
Classical Approach ◽  
Tensor Fields

In an intrinsic approach to a problem in elasticity, the only unknown is a tensor field representing an appropriate ‘measure of strain’, instead of the displacement vector field in the classical approach. The objective of this paper is to study the displacement traction problem in the special case where the elastic body is a linearly elastic plate of constant thickness, clamped over a portion of its lateral face. In this respect, we first explicitly compute the intrinsic three-dimensional boundary condition of place in terms of the Cartesian components of the linearized strain tensor field, thus avoiding the recourse to covariant components in curvilinear coordinates and providing an interesting example of actual computation of an intrinsic boundary condition of place in three-dimensional elasticity. Second, we perform a rigorous asymptotic analysis of the three-dimensional equations as the thickness of the plate, considered as a parameter, approaches zero. As a result, we identify the intrinsic two-dimensional equations of a linearly elastic plate modelled by the Kirchhoff–Love theory, with the linearized change of metric and change of curvature tensor fields of the middle surface of the plate as the new unknowns, instead of the displacement field of the middle surface in the classical approach.

Development of Three-Dimensional PML Boundary Conditions for Aeroacoustics Applications

2002 ◽  
Vol 1 (3) ◽  
pp. 307-327
Author(s):  
J-F. Dietiker ◽  
K.A. Hoffmann ◽  
M. Papadakis ◽  
R. Agarwal
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Perfectly Matched Layer ◽  
Optimum Combination ◽  
Curvilinear Coordinates ◽  
Main Program ◽  
Governing Equations ◽  
Compact Finite Difference ◽  
Finite Difference Formulation

Perfectly Matched Layer (PML) boundary conditions are derived in generalized curvilinear coordinates for three-dimensional aeroacoustic applications. The resulting governing equations are solved numerically by a four-stage Runge-Kutta scheme, with 4th/6th order compact finite difference formulation. The PML equations are programmed in a subroutine, which is easily incorporated to the main program LINEULER (Linearized Euler's equation solver). Two and three-dimensional benchmarks problems are solved to investigate the efficiency and accuracy of the PML boundary conditions. Investigations on the PML parameters have been conducted to determine the optimum combination of parameters used in the computations.

Propagation and Reflection of Plane Waves in a Rotating Magneto-Elastic Fibre-Reinforced Semi Space with Surface Stress

2020 ◽  
Vol 22 (4) ◽  
pp. 939-958
Author(s):  
Indrajit Roy ◽  
D. P. Acharya ◽  
Sourav Acharya
Keyword(s):  
Surface Stress ◽  
Incident Angle ◽  
Plane Waves ◽  
Three Dimensional ◽  
Elastic Fibre ◽  
Amplitude Ratios ◽  
Governing Equations ◽  
Rotation Surface ◽  
Wave Velocities ◽  
Magnetic Field Rotation

AbstractThe present paper investigates the propagation of quasi longitudinal (qLD) and quasi transverse (qTD) waves in a magneto elastic fibre-reinforced rotating semi-infinite medium. Reflections of waves from the flat boundary with surface stress have been studied in details. The governing equations have been used to obtain the polynomial characteristic equation from which qLD and qTD wave velocities are found. It is observed that both the wave velocities depend upon the incident angle. After imposing the appropriate boundary conditions including surface stress the resultant amplitude ratios for the total displacements have been obtained. Numerically simulated results have been depicted graphically by displaying two and three dimensional graphs to highlight the influence of magnetic field, rotation, surface stress and fibre-reinforcing nature of the material medium on the propagation and reflection of plane waves.

Microstructures of Low Angle Boundaries of the Second Generation Single Crystal Superalloy DD6

2011 ◽  
Vol 284-286 ◽  
pp. 1584-1587
Author(s):  
Zhen Xue Shi ◽  
Jia Rong Li ◽  
Shi Zhong Liu ◽  
Jin Qian Zhao
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
Scanning Electron Microscope ◽  
Thin Layer ◽  
Single Crystal ◽  
Second Generation ◽  
Three Dimensional ◽  
Single Crystal Superalloy ◽  
Transition Electron ◽  
Scanning Electron

The specimens of low angle boundaries were machined from the second generation single crystal superalloy DD6 blades. The microstructures of low angle boundaries (LAB) were investigated from three scales of dendrite, γ′ phase and atom with optical microscopy (OM), scanning electron microscope (SEM), transition electron microscope (TEM) and high resolution transmission electrion microscopy (HREM). The results showed that on the dendrite scale LAB is interdendrite district formed by three dimensional curved face between the adjacent dendrites. On the γ′ phase scale LAB is composed by a thin layer γ phase and its bilateral imperfect cube γ′ phase. On the atom scale LAB is made up of dislocations within several atom thickness.

Effects of moving lid direction on mixed convection and entropy generation in a cubical cavity with longitudinal triangular fin insertion

2017 ◽  
Vol 27 (4) ◽  
pp. 839-860 ◽  
Author(s):  
Lioua Kolsi ◽  
Hakan F. Öztop ◽  
Nidal Abu-Hamdeh ◽  
Borjini Mohamad Naceur ◽  
Habib Ben Assia
Keyword(s):  
Mixed Convection ◽  
Entropy Generation ◽  
Three Dimensional ◽  
Thermal Conductivity Ratio ◽  
Governing Equations ◽  
Content Type ◽  
Driven Cavity ◽  
Triangular Fin ◽  
Cubical Cavity ◽  
3D Problem

Purpose The main purpose of this work is to arrive at a three-dimensional (3D) numerical solution on mixed convection in a cubic cavity with a longitudinally located triangular fin in different sides. Design/methodology/approach The 3D governing equations are solved via finite volume technique by writing a code in FORTRAN platform. The governing parameters are chosen as Richardson number, 0.01 ≤ Ri ≤ 10 and thermal conductivity ratio 0.01 ≤ Rc ≤ 100 for fixed parameters of Pr = 0.7 and Re = 100. Two cases are considered for a lid-driven wall from left to right (V+) and right to left (V−). Findings It is observed that entropy generation due to heat transfer becomes dominant onto entropy generation because of fluid friction. The most important parameter is the direction of the moving lid, and lower values are obtained when the lid moves from right to left. Originality The main originality of this work is to arrive at a solution of a 3D problem of mixed convection and entropy generation for lid-driven cavity with conductive triangular fin attachments.

Fabrication of thin-layer matrigel-based constructs for three-dimensional cell culture

2018 ◽  
Vol 35 (1) ◽  
pp. e2733 ◽  
Author(s):  
Kristin Robin Ko ◽  
Meng-Chiao Tsai ◽  
John P. Frampton
Keyword(s):  
Cell Culture ◽  
Thin Layer ◽  
Three Dimensional ◽  
Dimensional Cell

scholarly journals Numerical Calculation of Flow for Cascade With Tip Clearance

1994 ◽  
Author(s):  
Shimpei Mizuki ◽  
Hoshio Tsujita
Keyword(s):  
Three Dimensional ◽  
Tip Clearance ◽  
Turbine Cascade ◽  
Governing Equations ◽  
Tensor Form ◽  
Pressure Surface ◽  
Rear Part ◽  
Blade Tip ◽  
Flow Through ◽  
Blade Tip Geometry

Three-dimensional incompressible turbulent flow within a linear turbine cascade with tip clearance is analyzed numerically. The governing equations involving the standard k-ε model are solved in the physical component tensor form with a boundary-fitted coordinate system. In the analysis, the blade tip geometry is treated accurately in order to predict the flow through the tip clearance in detail when the blades have large thicknesses. Although the number of grids employed in the present study is not enough because of the limitation of computer storage memory, the computed results show good agreements with the experimental results. Moreover, the results clearly exhibit the locus of minimum pressure on the rear part of the pressure surface at the blade tip.

Review of Three Dimensional Dynamic Analyses of Circular Cylinders and Cylindrical Shells

1994 ◽  
Vol 47 (10) ◽  
pp. 501-516 ◽  
Author(s):  
Kostas P. Soldatos
Keyword(s):  
Cylindrical Shells ◽  
Three Dimensional ◽  
Circular Cylinders ◽  
Accurate Information ◽  
Two Dimensional ◽  
Governing Equations ◽  
Complicated Form ◽  
Dynamic Analyses ◽  
Cylindrical Panels ◽  
Elastic Cylinders

There is an increasing usefulness of exact three-dimensional analyses of elastic cylinders and cylindrical shells in composite materials applications. Such analyses are considered as benchmarks for the range of applicability of corresponding studies based on two-dimensional and/or finite element modeling. Moreover, they provide valuable, accurate information in cases that corresponding predictions based on that later kind of approximate modeling is not satisfactory. Due to the complicated form of the governing equations of elasticity, such three-dimensional analyses are comparatively rare in the literature. There is therefore a need for further developments in that area. A survey of the literature dealing with three-dimensional dynamic analyses of cylinders and open cylindrical panels will serve towards such developments. This paper presents such a survey within the framework of linear elasticity.

Sign in / Sign up

Export Citation Format

Share Document