Stochastic responses of Navier-Stokes equations computed with dynamically orthogonal field equations

AbstractWe continue our study of the adaptation from spherical to doubly periodic slot domains of the poloidal-toroidal representation of vector fields. Building on the successful construction of an orthogonal quinquepartite decomposition of doubly periodic vector fields of arbitrary divergence with integral representations for the projections of known vector fields and equivalent scalar representations for unknown vector fields (Part 1), we now present a decomposition of vector field equations into an equivalent set of scalar field equations. The Stokes equations for slow viscous incompressible fluid flow in an arbitrary force field are treated as an example, and for them the application of the decomposition uncouples the conservation of momentum equation from the conservation of mass constraint. The resulting scalar equations are then solved by elementary methods. The extension to generalised Stokes equations resulting from the application of various time discretisation schemes to the Navier-Stokes equations is also solved.

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THE HYDRODYNAMICS OF ATOMS OF SPACETIME: GRAVITATIONAL FIELD EQUATION IS NAVIER–STOKES EQUATION

International Journal of Modern Physics D ◽

10.1142/s0218271811020603 ◽

2011 ◽

Vol 20 (14) ◽

pp. 2817-2822 ◽

Cited By ~ 3

Author(s):

T. PADMANABHAN

Keyword(s):

Gravitational Field ◽

Stokes Equations ◽

Navier Stokes ◽

Field Equations ◽

Gravitational Field Equation ◽

Navier Stokes Equation ◽

Navier Stokes Equations ◽

Gravitational Field Equations ◽

Conceptual Status ◽

Null Surface

There is considerable evidence to suggest that field equations of gravity have the same conceptual status as the equations of hydrodynamics or elasticity. We add further support to this paradigm by showing that Einstein"s field equations are identical in form to Navier–Stokes equations of hydrodynamics, when projected on to any null surface. In fact, these equations can be obtained directly by extremizing of entropy associated with the deformations of null surfaces thereby providing a completely thermodynamic route to gravitational field equations. Several curious features of this remarkable connection (including a phenomenon of "dissipation without dissipation") are described and the implications for the emergent paradigm of gravity is highlighted.

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On Boundary Conditions for Incompressible Navier-Stokes Problems

Applied Mechanics Reviews ◽

10.1115/1.2177683 ◽

2006 ◽

Vol 59 (3) ◽

pp. 107-125 ◽

Cited By ~ 52

Author(s):

Dietmar Rempfer

Keyword(s):

Boundary Conditions ◽

Stokes Equations ◽

Review Article ◽

Navier Stokes ◽

Field Equations ◽

Navier Stokes Equations ◽

Pressure Poisson Equation ◽

Flow Problems ◽

Stokes Problems ◽

Physical Boundary

We revisit the issue of finding proper boundary conditions for the field equations describing incompressible flow problems, for quantities like pressure or vorticity, which often do not have immediately obvious “physical” boundary conditions. Most of the issues are discussed for the example of a primitive-variables formulation of the incompressible Navier-Stokes equations in the form of momentum equations plus the pressure Poisson equation. However, analogous problems also exist in other formulations, some of which are briefly reviewed as well. This review article cites 95 references.

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Remarks on the asymptotic behaviour of solutions to the compressible Navier–Stokes equations in the half-line

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s030821050200032x ◽

2002 ◽

Vol 132 (03) ◽

pp. 627

Keyword(s):

Asymptotic Behaviour ◽

Stokes Equations ◽

Half Line ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Asymptotic Behaviour Of Solutions

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Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES ◽

10.15282/jmes.14.4.2020.05.0579 ◽

2020 ◽

Vol 14 (4) ◽

pp. 7369-7378

Author(s):

Ky-Quang Pham ◽

Xuan-Truong Le ◽

Cong-Truong Dinh

Keyword(s):

Stokes Equations ◽

Three Dimensional ◽

Axial Compressor ◽

Aerodynamic Performance ◽

Numerical Results ◽

Single Stage ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Operating Stability ◽

Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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