Mathematical modelling of two-dimensional turbulent flow in curvilinear coordinate systems
- Authors: Slavko GERČER
- Citation: Acta hydrotechnica, vol. 18, no. 28, pp. 3-40, 2000.
- Abstract: In the first part of the thesis, a mathematical derivation of the dynamic and the mass conservation equation in curvilinear coordinate system is presented. The mean purpose of the derivation of equations is to establish the basics of the first approach for the solving of the equations which, in their transformed form, are later used in a curvilinear coordinate system. In the second part, the so- called second approach is derived, where the equations are solved in a non-transformed form.The numerical discretisation of the dynamic and mass conservation equations in the orthogonal grid is interpreted. The theoretical derivation of the numerical discretisation of equations for trapezoidal cells is described using a finite volume method. Afterwards, a new mathematical model (PCFLOW2D-CURVE) which enables the modelling of flow for any optional structure of numerical grid was developed. A new software (GEO-CURVE) in the CADD environment was developed to generate a numerical grid for any optional form of the riverbed. The thesis gives a review and basic principles of solving the equations in a curvilinear coordinate system. Therefore, it can be used as a good mathematical basis for the further development of curvilinear models.
- Keywords: mathematical models, two-dimensional modelling, numerical methods, finite volume method, curvilinear coordinate system
- Full text: a28-sg.pdf