Document Type

Thesis

Department

Mechanical Engineering

Advisor's Name

Igor Tsukanov

Advisor's Title

Committee Chair

Advisor's Name

George Dulikravich

Advisor's Name

Yiding Cao

Keywords

Transient, nonlinear, meshfree, heat transfer, Oseen, Newton-Kantorovich, linearize, Galerkin, temperature-dependent

Date of Defense

11-9-2010

Abstract

In the presented thesis work, meshfree method with distance fields was extended to obtain solution of nonlinear transient heat transfer problems. The thesis work involved development and implementation of numerical algorithms, data structure, and software. Numerical and computational properties of the meshfree method with distance fields were investigated. Convergence and accuracy of the methodology was validated by analytical solutions, and solutions produced by commercial FEM software (ANSYS 12.1). The research was focused on nonlinearities caused by temperature-dependent thermal conductivity. The behavior of the developed numerical algorithms was observed for both weak and strong temperature-dependency of thermal conductivity. Oseen and Newton-Kantorovich linearization techniques were applied to linearized the governing equation and boundary conditions. Results of the numerical experiments showed that the meshfree method with distance fields has the potential to produced fast accurate solutions. The method enables all prescribed boundary conditions to be satisfied exactly.

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