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This course leads students to proficiency in the mathematical and numerical modelling of heat and mass transfer for the hygrothermal design of buildings, building zones and building components. Some applications include ventilation flows, thermal stratification, interior moisture buffering, interstitial condensation, and driving rain absorption. The course covers the mathematical models for discrete/continuum, steady-state/transient, and potential/non-potential heat, air and moisture transfer. Through the translation of physical phenomena into mathematical equations, students are exposed to the underlying limitations and simplifications of numerical modelling. Control volumes and finite elements for spatial discretisation and finite differences for temporal discretisation are presented. Their accuracy, reliability, efficiency and suitability are discussed. Linearization approaches, such as the Picard and Newton-Raphson methods, are introduced and complemented with exercises in convergence criteria. Verification of developed code by comparison to analytical or other numerical solutions are addressed, along with model validation by comparison to experimental data. Students practice implementation and application of numerical models and discuss efficient programming. Some ready-made numerical simulation platforms are introduced.
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