Building physics with numerical applications

The course mainly describes how to solve nonlinear partial differential equations. The equations describe time-dependent heat transport and moisture transport problems applied in the building construction contexts. The background to the governing equations is explained with help of the combination of physical balance equations and constitutive relations. Solutions to equations are developed using the finite element method for different types of boundary conditions and initial conditions. The finite element method is formulated in such a way that time-dependent equations can be solved, which means that the time is discretized in addition to the spatial discretization. Since moisture transport problems in particular are both a coupled and non-linear problem, a solution strategy is required where the residual to the equations can be minimized using the Newton-Raphson method. Derivation of the tangential stiffness in this type of nonlinear and coupled problems is explained in detail.