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APPLICATION OF SUNDIALS TO SOLVE PHASE FIELD EQUATIONS DESCRIBING DENDRITIC SOLIDIFICATION IN MULTI-COMPONENT ALLOY SYSTEMS

IP.com Disclosure Number: IPCOM000236782D
Publication Date: 2014-May-15
Document File: 7 page(s) / 88K

Publishing Venue

The IP.com Prior Art Database

Abstract

The invention proposes a technique for predicting microsegregation, microstructure length scales and optimizes microstructure through chemistry of alloy and process control. Once the free energies describing solid and liquid phases are obtained using CALPHAD, the technique solves non linear algebraic equations defining equal chemical potential condition at the solid-liquid interface. Using an algorithm non linear partial differential equations and algebraic equations are solved simultaneously without interfacing with any external software.

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APPLICATION OF SUNDIALS TO SOLVE PHASE FIELD EQUATIONS DESCRIBING DENDRITIC SOLIDIFICATION IN MULTI-COMPONENT ALLOY SYSTEMS

BRIEF ABSTRACT

The invention proposes a technique for predicting microsegregation, microstructure length scales and optimizes microstructure through chemistry of alloy and process control. Once the free energies describing solid and liquid phases are obtained using CALPHAD, the technique solves non linear algebraic equations defining equal chemical potential condition at the solid-liquid interface. Using an algorithm non linear partial differential equations and algebraic equations are solved simultaneously without interfacing with any external software.

KEYWORDS

SUNDIALS, multi-component alloy system, CALPHAD


DETAILED DESCRIPTION

SUNDIALS, which stands for suite of nonlinear and dIfferential/algebraic equation solvers, is an open-source library of non-linear solvers developed for robust and time efficient numerical solution for non-linear phase field equations. The phase field model is extensively applied to study dendritic growth and microsegregation during solidification. The approach is suitable for complex moving boundary problems involving microstructural evolution as it does not involve explicit tracking of interfaces.

Several attempts are made at solving the problem of multi-component solidification using phase field method.

A conventional technique includes a fully implicit numerical method, based upon a combination of adaptively re-fined hierarchical meshes and geometric multigrid. The method is presented for simulation of binary alloy solidification in three space dimensions. In our work we intend to simulate binary alloy solidification using Newton-krylov solver in SUNDIALS.

Another conventional technique includes a system of phase field partial differential equations (PDEs) which are solved simultaneously together with PDEs describing additional physics, such as, solid mechanics and heat conduction, using Jacobian-Free Newton Krylov Method. Our solver solves the phase field equation and diffusion equation (non linear heat condution equation) using Jacobian free Newton krylov solver.

However, the above mentioned conventional techniques are limited to explicit procedures or computationally expensive control volume methods.

Therefore, there is need for an efficient technique to solve phase field equations describing dendritic solidification in multi-component alloy systems using SUNDIALS.

The invention proposes a technique for predicting microsegregation, microstructure length scales and optimizes microstructure through chemistry of alloy and process control.

Modeling solidification using phase field method requires a set of coupled equations. The equations include nonlinear phase field equation describing the liquid-solid transformation and a set of nonlinear diffusion equations describing the diffusional transport of components within the liquid and solid phases. The technique assumes equal chemical potential...