Regular Article: An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries

After a brief review of current source-based methods for modeling solidification phase change systems, a new source-based method for the treatment of latent heat evolution is presented. The essential feature of the proposed method is linearization of the discretized source term. This results in a robust and accurate computational method that can deal efficiently with a wide range of latent heat evolution mechanisms (i.e., liquid fraction temperature relationships). The proposed method is illustrated on application to a test problem in which various liquid fraction temperature relationships are employed.

Eral source-based method for solidification phase change

SUMMARY The aim of this paper is to categorize the major fixed grid formulations and solution methods for conduction controlled phase change problems. Using a two phase model of. a solid/liquid phase change, the basic enthalpy equation is derived. Starting from this equation, a number of alternative formulations are obtained. All the formulations are reduced to a standard form. From this standard form, finite element and finite volume discretizations are developed. These discretizations are used as the basis for a number of fixed grid numerical solution techniques for solidification phase change systems. In particular, various apparent capacity and source based enthalpy methods are explored.

Fixed grid techniques for phase change problems: A review

Modelling of heat flow has become a standard practice in many solidification processes. Effort is currently being made to couple heat flow calculations to related macroscopic phenomena such as mould filling, fluid flow, macrosegregation, or thermal stresses. If these macroscopic aspects are important in predicting formation of macroscopic defects or optimising process conditions, then microstructural features such as phase appearance, morphology, grain size, spacings, or microdefects are certainly no less important in determining the ultimate mechanical properties of the solidified product. The aim of the present paper is to introduce the basic concepts of macroscopic and microscopic phenomena which enter normally into any solidification process. At the macroscopic level, i.e. at the scale of the whole process (casting, weldment, … ), the latest developments in numerical techniques which are used to solve the continuity equations are briefly presented together with the advantages and inconvenience...

Modelling of microstructure formation in solidification processes

http://lmee.univ-evry.fr/~olm/biblio_dwnload/jcp_stoch2.pdf

A stochastic projection method for fluid flow II.: random process

The finite element method is employed for the analysis of velocity and temperature distributions in refrigerated open display cabinets. The CFD code is based on the streamfunction-vorticity formulation, and incorporates a LES turbulence model. As an example of application, a vertical multi-deck cabinet is investigated under different operating conditions. The numerical results have been validated by comparison with experimental tests performed in accordance with the EN441 Standard. The influence of various design parameters has been investigated.

CFD simulation of refrigerated display cabinets

The finite element method, formulated for non-linear heat conduction, allows the solution of practically any ground freezing problem. Stabilization of wet soils by artificial freezing and freezing under roads induced by cold winter conditions are considered in this paper.



Special features of the program used include parabolic isoparametric elements, a new time stepping scheme and an improved procedure for the estimation of thermal properties.

Finite element simulation of freezing processes in soils

Laminar forced convection in ducts

A finite-element procedure is presented for the calculation of two-dimensional, viscous, incompressible flows of a recirculating nature. As in finite-difference procedures, velocity and pressure are uncoupled and the equations are solved one after the other. Velocity fields are determined by first calculating intermediate velocity values based on an estimated pressure distribution and then obtaining appropriate corrections to satisfy the continuity equation. Illustrative examples involving flow in the entrance region between parallel plates, lid-driven cavity flow, and flow around an obstacle demonstrate the accuracy and capabilities of the proposed technique.

Finite-element solution of the incompressible navier-stokes equations

A finite-element algorithm is presented for the solution of two- and three-dimensional incompressible laminar thermal flows. The algorithm is cast in a time-dependent form and can be classified as a projection finite-element method. However, the procedure utilized for handling Ike velocity-pressure coupling shares many features with the SIMPLER finite-difference method. In fact, given an initial or guessed velocity field, the pseudo-velocities, i.e., the velocities that would prevail in the absence of the pressure field, are found first. Then, by enforcing continuity on the pseudo-velocity field, the tentative pressure is estimated and the momentum equations are solved in sequence for the velocity components. Afterward, continuity is enforced again to find corrections that are used to modify the velocity field and the estimated pressure field. Finally, if required, the energy equation is solved before moving to the next step.

Gianni Comini

Papers

CFD simulation of refrigerated display cabinets

Finite element simulation of freezing processes in soils

Laminar forced convection in ducts

Finite-element solution of the incompressible navier-stokes equations

An equal-order velocity-pressure algorithm for incompressible thermal flows, part 1: Formulation