A global analysis approach to the general relativistic fluid ball problem

1980 ◽  
Vol 12 (2) ◽  
pp. 155-174 ◽  
Author(s):  
H. P. Künzle ◽  
J. R. Savage
Keyword(s):  
Global Analysis ◽  
Analysis Approach ◽  
Relativistic Fluid ◽  
Fluid Ball ◽  
Ball Problem ◽  
General Relativistic

scholarly journals Minkowski and Galilei/Newton Fluid Dynamics: A Geometric 3 + 1 Spacetime Perspective

Fluids ◽  
2018 ◽  
Vol 4 (1) ◽  
pp. 1 ◽  
Author(s):  
Christian Cardall
Keyword(s):  
Fluid Dynamics ◽  
Particle Number ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Balance Equations ◽  
Tensor Decompositions ◽  
Relativistic Fluid ◽  
Stress Energy ◽  
General Relativistic ◽  
Classical Particles

A kinetic theory of classical particles serves as a unified basis for developing a geometric 3 + 1 spacetime perspective on fluid dynamics capable of embracing both Minkowski and Galilei/Newton spacetimes. Parallel treatment of these cases on as common a footing as possible reveals that the particle four-momentum is better regarded as comprising momentum and inertia rather than momentum and energy; and, consequently, that the object now known as the stress-energy or energy-momentum tensor is more properly understood as a stress-inertia or inertia-momentum tensor. In dealing with both fiducial and comoving frames as fluid dynamics requires, tensor decompositions in terms of the four-velocities of observers associated with these frames render use of coordinate-free geometric notation not only fully viable, but conceptually simplifying. A particle number four-vector, three-momentum (1, 1) tensor, and kinetic energy four-vector characterize a simple fluid and satisfy balance equations involving spacetime divergences on both Minkowski and Galilei/Newton spacetimes. Reduced to a fully 3 + 1 form, these equations yield the familiar conservative formulations of special relativistic and non-relativistic fluid dynamics as partial differential equations in inertial coordinates, and in geometric form will provide a useful conceptual bridge to arbitrary-Lagrange–Euler and general relativistic formulations.

General relativistic fluid spheres with variable polytropic index

1966 ◽  
Vol 6 (2) ◽  
pp. 139-147
Author(s):  
R. van der Borght
Keyword(s):  
General Relativity ◽  
Compressible Fluid ◽  
Fluid Sphere ◽  
Polytropic Index ◽  
Field Equations ◽  
Relativistic Fluid ◽  
General Relativistic ◽  
Temperature And Pressure ◽  
Fluid Spheres

AbstractIn this paper we derive solutions of the field equations of general relativity for a compressible fluid sphere which obeys density-temperature and pressure-temperature relations which allow for a variation of the polytropic index throughout the sphere.

Comparative Study of Drilling Riser Running/Retrieving Analysis Methodologies

2021 ◽  
Author(s):  
Leandro Vale ◽  
Conor Gallagher ◽  
Marcelo Souza ◽  
Daniel Carneiro
Keyword(s):  
Complex Geometry ◽  
Global Analysis ◽  
Fe Analysis ◽  
Analysis Approach ◽  
Harsh Environment ◽  
Local Response ◽  
Offshore Drilling ◽  
Global Response ◽  
Offshore Oil ◽  
Water Depths

Abstract Drilling risers are key components in offshore oil exploration and are present in most of the well construction phases (drilling, casing, cementing and completion). Mobile offshore drilling units can operate in different sites exposed to a range of environmental loadings and water depths. Global riser analyses based on the FE (finite element) method are performed to assess the system feasibility and operating envelopes. In harsh environment and ultradeep water scenarios, the riser running/retrieving operation is one of the most critical due to top-angle limits and riser stress as a result of either contact with the inside of the diverter housing/substructures or loading at the gimbal-spider (API-RP-16Q [1], ISO 13624-1 [2]). The use of beam-column elements is satisfactory for modelling the riser global response, however it may lead to result uncertainty in terms of local response associated with complex geometry, over-stress, stress concentration and contact modelling (DNV-ST-F201 [3], DNVGL-RP-F203 [4], ISO 13628-7 [5]). The objective of this paper is to compare riser analysis results from a global and a local FE analysis. This comparison is used to identify any limitations associated with the use of a global riser analysis approach for determining structural limits for the riser during deployment/retrieving operations. Several recommendations are also provided regarding the use of the global analysis approach.

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