Strong Conservative Form of the Incompressible Navier–Stokes Equations in a Rotating Frame with a Solution Procedure

Beddhu, Murali; Taylor, Lafayette K.; Whitfield, David L.

doi:10.1006/jcph.1996.0221

Cited by 32 publications

(34 citation statements)

References 9 publications

(22 reference statements)

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“…This conservative formulation has been developed and used successfully to simulate the flow in non-inertial reference frames (Beddhu et al, 1996;Kim and Choi, 2006). Note that, as shown by Kim and Choi (Kim and Choi, 2006), the non-conservative formulation is not adopted herein because it can lead to severe instability in the numerical method.…”

Section: The Governing Equations and Boundary Conditionsmentioning

confidence: 99%

On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming

Borazjani

Sotiropoulos

2010

Journal of Experimental Biology

223

195

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SUMMARYWe carry out fluid-structure interaction simulations of self-propelled virtual swimmers to investigate the effects of body shape (form) and kinematics on the hydrodynamics of undulatory swimming. To separate the effects of form and kinematics, we employ four different virtual swimmers: a carangiform swimmer (i.e. a mackerel swimming like mackerel do in nature); an anguilliform swimmer (i.e. a lamprey swimming like lampreys do in nature); a hybrid swimmer with anguilliform kinematics but carangiform body shape (a mackerel swimming like a lamprey); and another hybrid swimmer with carangiform kinematics but anguilliform body shape (a lamprey swimming like a mackerel). By comparing the performance of swimmers with different kinematics but similar body shapes we study the effects of kinematics whereas by comparing swimmers with similar kinematics but different body shapes we study the effects of form. We show that the anguilliform kinematics not only reaches higher velocities but is also more efficient in the viscous (Re~10 2 ) and transitional (Re~10 3 ) regimes. However, in the inertial regime (Reϱ) carangiform kinematics achieves higher velocities and is also more efficient than the anguilliform kinematics. The mackerel body achieves higher swimming speeds in all cases but is more efficient in the inertial regime only whereas the lamprey body is more efficient in the transitional regime. We also show that form and kinematics have little overall effect on the 3-D structure of the wake (i.e. single vs double row vortex streets), which mainly depends on the Strouhal number. Nevertheless, body shape is found to somewhat affect the small-scale features and complexity of the vortex rings shed by the various swimmers.

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Section: The Governing Equations and Boundary Conditionsmentioning

confidence: 99%

On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming

Borazjani

Sotiropoulos

2010

Journal of Experimental Biology

223

195

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“…Also, re-generation of computational grid is needed every time the objects translate, which often increases the computation load significantly. This problem is partially resolved by employing a body-fixed non-inertial treatment (1), (2) or arbitrary Lagrangian-Eulerian approach (3) . However, these approaches resolving the flow field with body-fitted coordinates are no longer applicable to the system where free movements of poly-sized particles (meshing over multiple-connected regions) or contacting of the multiple objects is dominant.…”

Section: Introductionmentioning

confidence: 99%

Efficient Immersed Boundary Method for Strong Interaction Problem of Arbitrary Shape Object with the Self-Induced Flow

Yuki

Takeuchi

Kajishima

2007

JFST

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An immersed boundary method is improved and applied to 2-D flow fields involving a single stationary/moving object. The present immersed boundary method employs a body force proportional to a solid volume fraction for coupling the solid and fluid motions at the interface. A hyperbolic-tangent function is newly introduced as a surface digitiser for computing the volume fractions at the interface cells, and this improvement is proved to be efficient for problems involving arbitrary shape object. The present method is applied to a uniform flow field around a circular cylinder and an interaction problem of fluid and free-falling object. The computational results are found to agree with the results by the different methods of the present authors and the results reported in the literatures. Also the computation time is considerably cut down compared to the other methods by the series of improvements to the immersed boundary method.

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“…Takakura (4) incorporated the effect of the translation of the coordinate system into an apparent force of the compressible N-S equations. Also, in geophysics, N-S equations in a rotating frame with a constant angular velocity are often used (5) .…”

Section: Introductionmentioning

confidence: 99%

“…However, the time derivative of the Euler angles could become singular when the zenithal angle approaches zero or 180 degrees, which results in atypical behaviours of the object and, in turn, the non-physical interaction with the fluid. Another reason may be that the apparent forces may cause some numerical instability since they appear as source term in the N-S equations (5) . This numerical instability will be severe particularly near the outer boundary when the object rotates at a high angular velocity.…”

Section: Introductionmentioning

confidence: 99%

“…This numerical instability will be severe particularly near the outer boundary when the object rotates at a high angular velocity. One possible solution may be incorporating part of the apparent forces into the conservative form (5), (6) . This treatment modifies the boundary condition at the body surface to include the frame rotation, and therefore, near field behaviour of the fluid will be sensitive to the accuracy of rotation matrix.…”

Section: Introductionmentioning

confidence: 99%

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Study of Solid-Fluid Interaction in Body-Fixed Non-Inertial Frame of Reference

Takeuchi

Yamazaki

Kajishima

2006

JFST

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Motion of solid object in fluid is studied in moving frame of reference. Navier-Stokes (N-S) equations in a non-inertial frame of reference is coupled with the equations of linear and angular momentums for the solid object. It is shown that the numerical implementation for solving the non-inertial N-S equations is equivalent to that of the arbitrary Lagrangian-Eulerian (ALE) method. The simulation results by the two methods show reasonable agreements for a 2-D flow field including a cylinder. In the present work, a generalised convective boundary condition is constructed for non-inertial frame of reference. Also, an appropriate boundary condition is proposed for fluid phase based on a least square adjustment (LSA) method. It is shown that the LSA is essential for the non-inertial study fluid-solid interaction. Also, the noninertial N-S equation is applied to a problem of a concave object falling in a fluid. It is shown that traditional time-advancement schemes undermine the ortho-normality of the rotation matrix, resulting in non-physical deformation of the object. However, our time-advancement procedure with quaternion is found to be robust and effective even under a violent manoeuvre of the object.

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Strong Conservative Form of the Incompressible Navier–Stokes Equations in a Rotating Frame with a Solution Procedure

Cited by 32 publications

References 9 publications

On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming

On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming

Efficient Immersed Boundary Method for Strong Interaction Problem of Arbitrary Shape Object with the Self-Induced Flow

Study of Solid-Fluid Interaction in Body-Fixed Non-Inertial Frame of Reference

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