Modelování teplotně stratifikovaného proudění v atmosféře

Abstract

In this thesis there is simulated an incompressible laminar flow in a higher-order accuracy around a circle cylinder with usage of an immersed boundary method and around a cylinder with a square cross-section with an influence of a thermal stratification. In the theoretical part the system of Navier-Stokes equations with Bussinesq approximation is derived and the methods for simulating are described. Fifth order WENO shock-capturing scheme reconstructs advections terms on the boundaries of control volumes. An explicit fourth-order Runge-Kutta scheme solves the first step of a fractional steps method. The obstacle with the circle cross-section is described by the immersed boundary method. In the implementation section there is interpreted the structure of programs for 2D cases. In the section Numerical experiments there is realized testing of the examples with the exactknown results the linear hyperbolic equations, the Burgers equations and the Euler equations and of a square cavity flow with Reynolds numbers of 100,1000 and 5000 with known numerical results for the Navier-Stokes equation. There is solved the flow around a square (and a circle) cylinder for Reynolds numbers 30; 200. Strouhal numbers are computed for von Kármán vortex street. Finally the flow around a square cylinder with influence of thermal...