Fundamental approach to anisotropic heat conduction using the element-based finite volume method

This work describes the fundamentals of the element-based finite volume method for anisotropic heat conduction within the framework of the finite element space. Patch tests indicate no element inconsistencies or deficiencies when facing mesh distortion and poor aspect ratio. Convergence and accuracy assessments show that the method presents asymptomatic rate of convergence with discretization errors approaching a second-order scheme. Anisotropic heat conduction in a periodical solid lattice illustrates the application of the method. Application of an optimization technique demonstrates that the choice of a proper material orientation when manufacturing the solid lattice can increase the global heat transfer coefficient.