Computation of Solid–Liquid Phase Fronts in the Sharp Interface Limit on Fixed Grids

Udaykumar, H. S.; Mittal, Rajat; Shyy, Wei

doi:10.1006/jcph.1999.6294

Cited by 320 publications

(279 citation statements)

References 52 publications

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“…For sharp interface methods, one issue encountered with moving boundaries is the so called "fresh-cell" problem [44,45]. This refers to the situation where a cell that is in the solid at one time step, emerges into the fluid at the next time-step due to boundary motion.…”

Section: Boundarymentioning

confidence: 99%

“…These include methods of Udaykumar et al [44], Ye et al [51], Fadlun et al [9], Kim et al [16], Gibou et al [12], You et al [52], Balaras [2], Marella et al [22], Ghias et al [11] and others. The key advantage of the first category of methods is that they are formulated relatively independent of the spatial discretization and therefore can be implemented into an existing Navier-Stokes solver with relative ease.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries

Mittal

Dong

Bozkurttas

et al. 2008

Journal of Computational Physics

969

754

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A sharp interface immersed boundary method for simulating incompressible viscous flow past threedimensional immersed bodies is described. The method employs a multi-dimensional ghost-cell methodology to satisfy the boundary conditions on the immersed boundary and the method is designed to handle highly complex three-dimensional, stationary, moving and/or deforming bodies. The complex immersed surfaces are represented by grids consisting of unstructured triangular elements; while the flow is computed on non-uniform Cartesian grids. The paper describes the salient features of the methodology with special emphasis on the immersed boundary treatment for stationary and moving boundaries. Simulations of a number of canonical two-and three-dimensional flows are used to verify the accuracy and fidelity of the solver over a range of Reynolds numbers. Flow past suddenly accelerated bodies are used to validate the solver for moving boundary problems. Finally two cases inspired from biology with highly complex three-dimensional bodies are simulated in order to demonstrate the versatility of the method.

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Section: Boundarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries

Mittal

Dong

Bozkurttas

et al. 2008

Journal of Computational Physics

969

754

View full text Add to dashboard Cite

show abstract

“…The finite-difference stencil used to calculate the gradients at the interface may not be second-order accurate. Since these points are few in number, the deterioration in global accuracy below ) ( 2 x O  is expected to be minimal 13 [21].…”

Section: Solution Of the Governing Equationsmentioning

confidence: 99%

“…This problem is often used to validate numerical methods for phase-change (for example, see Refs. [13,21]). …”

Section: D Melting Problemmentioning

confidence: 99%

Fixed-Grid Front-Tracking Algorithm for Solidification Problems, Part I: Method and Validation

Garimella

Simpson

2003

Numerical Heat Transfer, Part B: Fundamentals

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This paper presents a method for solving moving boundary problems associated with phase-change. This method is an explicit interface-tracking scheme that involves the reconstruction and advection of the moving interface on a fixed grid. Three distinct steps are undertaken to handle the movement of the interface: advection and reconstruction (tracking); calculation of normal velocities; and the solution of the governing equations for different phases.Details of each step and its implementation is provided. The transient heat diffusion equation in two space dimensions is the governing equation for energy transport. In order to validate the approach, results obtained from the front tracking scheme are compared with exact analytical solutions for melting problems in Cartesian and cylindrical coordinates. It is shown that the numerical and analytical results are in excellent agreement. Finally, problems involving the multi-dimensional solidification of a pure aluminum ingot subject to bi-directional heat extraction are presented. The results indicate that the algorithm was able to accurately track the front under these aggressive conditions which caused large curvature. In Part II, the front-tracking approach described herein is applied to directional solidification problems influenced by melt convection.

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“…Similarly, as in Udaykumar et al, [27] for two-dimensional problems, the temperature gradients at each side of the interface are calculated using the following second-order finitedifference approximation:…”

Section: A Governing Equationsmentioning

confidence: 99%

High-Velocity Oxygen Fuel Thermal Spray of Fe-Based Amorphous Alloy: a Numerical and Experimental Study

Ajdelsztajn

Dannenberg

López

et al. 2009

Metall Mater Trans A

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The fabrication of dense coatings with appropriate properties using a high velocity oxygen fuel (HVOF) spray process requires an in-depth understanding of the complete gas flow field and particle behavior during the process. A computational fluid dynamics (CFD) model is implemented to investigate the gas flow behavior that occurs during the HVOF process and a simplified one-dimensional decoupled model of the in-flight thermal behavior of the amorphous Fe-based powder particles was developed and applied for three different spray conditions. The numerical results were used to rationalize the different coating microstructures described in the experimental results. Low porosity and amorphous coatings were produced using two different particle size distributions (16 to 25 lm and 25 to 53 lm). The amorphous characteristics of the powder were retained in the coating due to melting and rapid solidification in the case of very fine powder or ligaments (<16 lm) and to the fact that the crystallization temperature was not reached in the case of the large particles (16 to 53 lm).

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Computation of Solid–Liquid Phase Fronts in the Sharp Interface Limit on Fixed Grids

Cited by 320 publications

References 52 publications

A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries

A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries

Fixed-Grid Front-Tracking Algorithm for Solidification Problems, Part I: Method and Validation

High-Velocity Oxygen Fuel Thermal Spray of Fe-Based Amorphous Alloy: a Numerical and Experimental Study

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