C. R. Swaminathan

ERAL SOURCE-BASED METHOD FOR SOLIDIFICATION PHASE CHANGE

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.

A general enthalpy method for modeling solidification processes

In the present work, a general implicit source-based enthalpy method is presented for the analysis of solidification systems. The proposed approach is both robust and efficient. The performance of the method is illustrated by application to a number of problems taken from recent metallurgical literature.

Streamline upwind scheme for control-volume finite elements, part i. formulations

The basic features of the Galerkin and control-volume-based finite-element approximations are outlined. For convection-diffusion problems, these approximations could lead to unstable solutions. The streamline upwind Petrov Galerkin (SUPG) finite-element approach to overcome this problem is discussed. After this, extensions of the concepts in the SUPG approach are made to the control-volume-based finite-element method. The resulting streamline upwind control-volume (SUCV) finite-element method exhibits upwinding features similar to the SUPG method while retaining the conservative property of control-volume methods.

A time-implicit filling algorithm

Abstract The volume of fluid (VOF) equation is a well-known method for tracking the liquid/air interface during a filling process. Standard numerical approximations of the VOF equation fail to preserve a sharp interface. Methods that ensure a sharp interface in VOF calculations are investigated in this paper. At first, two previous VOF schemes that limit the smearing of the interface, via appropriate approximation of the convective flux, are outlined. These schemes are explicit in nature and hence subject to time step restrictions. A new scheme for approximating the convective flux is introduced. Implicit solutions based on this modified scheme are smear free and are not subject to any time step restrictions. Solutions to example filling problems are in close agreement with solutions based on traditional VOF approaches. Some potential drawbacks of the new method are investigated. In the context of filling problems it is shown that these drawbacks are not significant.

Treatment of discontinuous thermal conductivity in control-volume solutions of phase-change problems

Phase-change problems often involve discontinuities in the thermal properties at the phase-change boundary. This feature needs to be handled carefully when seeking a numerical solution based on a fixed space grid. Of particular concern are discontinuities in the thermal conductivity. In the context of a control-volume finite-difference solution, the requirement is an appropriate approximation of the conductivity values at the control-volume interfaces. In this article, using the Kirchhoff transformation, an approximation for the interface conductivity is developed. The approach is tested on a range of one- and two-dimensional, steady and transient phase-change problems. In addition, a discussion on the extension of the approach to finite-element schemes is included.

STREAMLINE UPWIND SCHEME FOR CONTROL-VOLUME FINITE ELEMENTS, PART II. IMPLEMENTATION AND COMPARISON WITH THE SUPG FINITE-ELEMENT SCHEME

The streamline upwind control-volume (SUCV) finite-element scheme is compared to the streamline upwind Petrov Galerkin (SUPG) finite-element scheme for a range of steady-state and transient test problems. The results indicate that for steady-state problems, the two schemes perform at the same level; while for transient convective problems, the SUPG scheme is slightly better. In addition, a qualitative performance comparison is made with previous control-volume finite-element schemes. These comparisons indicate that the performance of the SUCV scheme is competitive.

A streamline upwind control volume finite element method for modeling fluid flow and heat transfer problems

Abstract Galerkin and control volume finite element approximations are compared and contrasted. Streamline upwinding and pressure stabilizing Petrov-Galerkin formulations for the numerical modeling of fluid flow problems are discussed. These formulations are then adapted to a control volume finite element discretization. The resulting control volume finite element scheme permits an equal order interpolation for velocity and pressure, is readily implemented and retains the property of local conservation, normally associated with control volume schemes.

Cyclic phase change with fluid flow

Cyclic phase change involves the successive freezing and melting of a region driven by a boundary temperature that cycles above and below the solid/liquid phase change temperature. In this paper, a recently proposed fixed grid phase change enthalpy method is modified and applied to cyclic solid/liquid phase change problems. The basic approach is demonstrated on application to a one‐dimensional, heat conduction controlled phase change. Then the method is used to investigate a cyclic phase change problem that involves fluid flow. The interaction of the melting and freezing with the phase change leads to some interesting predictions for the location and shape of the solid/liquid interface. The results also indicate that melting cycles are more effective than freezing cycles.