A widely used dynamical core, PUMA (Portable University Model of the Atmosphere), is validated using the test case specifications introduced by Polvani et al. (2004). Dynamical cores are essential in every presently used AGCM (Atmospheric General Circulation Model), and deal with the dry, adiabatic primitive equations. The validation process is important in order to establish that the dynamical core is free from bugs, and thereby confirm the validity AGCMs. The test case proposed by Polvani et al. (2004) consists of a 12 day time-integrated slightly perturbed, baroclinically unstable, midlatitude jet, and is, together with derivations of the model equations, completely described in this M. Sc. thesis. The initial condition for the test case is implemented in PUMA, to a modification in order to carry out the same test case as in Polvani et al. (2004). The temperature and vorticity fields are presented and compared. The numerically converged solutions from PUMA are in strong accordance with the solutions from Polvani et al. (2004), despite different numerical schemes to solve the equations. This supports the validity and reliability for future studies with PUMA. / En torr, adiabatisk primitiv ekvationsmodell, PUMA (Portable University Model of the Atmosphere), valideras genom att jämföra dess lösningar med resultaten som presenterades av Polvani et al. (2004). Primitiva ekvationsmodeller är en viktig del i dagens allmänna cirkulationsmodeller. Valideringsprocessen är viktig för att fastslå att de primitiva ekvationsmodellerna fungerar utan buggar, och därigenom bekräfta att en viktig del av de allmänna cirkulationsmodellerna fungerar tillfredsställande. Initialtillståndet som presenterades av Polvani et al. (2004) består av en 12 dagars tids-integrerad, något perturberad, baroklint instabil polarjet. Initialtillståndet är, tillsammans med härledningarna av modellekvationerna, fullständigt beskriven i detta examensarbete. Initialtillståndet implementeras i PUMA, vilken har modifierats för att konstruera samma testspecifikationer som i Polvani et al. (2004). Temperatur- och virvlingsfälten presenteras och jämförs. De numeriskt konvergerade lösningarna från PUMA stämmer väl överrens med lösningarna från Polvani et al. (2004), trots att olika numeriska scheman använts för att lösa ekvationerna. Detta stödjer validiteten hos PUMA, vilket ökar tillförlitligheten i framtida studier med modellen.

The flow field and forces on an isolated oscillating NACA 0012 airfoil in a uniform flow is studied using viscous vortex particle method. The simulations are carried out at very low chord (c) based Reynolds number (Re=1000), motivated by the current interest in development of Micro Air Vehicles (MAV). The airfoil is forced to oscillate in both heave and pitch at different normalized oscillation frequencies (f), which is represented by the non-dimensional reduced frequency fc/U).( From the unsteady loading on the airfoil, the net energy transfer to the airfoil is calculated to determine the propensity for the airfoil to undergo self-induced oscillations or flutter at these very low Reynolds numbers. The simulations are carried out using a viscous vortex particle method that utilizes discrete vortex elements to represent the vorticity in the flow field. After validation of the code against test cases in the literature, simulations are first carried out for the stationary airfoil at different angles of attack, which shows the stall characteristics of the airfoil at this very low Reynolds numbers. For the airfoil oscillating in heave, the airfoil is forced to oscillate at different reduced frequencies at a large angle of attack in the stall regime. The unsteady loading on the blade is obtained at different reduced frequencies. This is used to calculate the net energy transfer to the airfoil from the flow, which is found to be negative in all cases studied. This implies that stall flutter or self-induced oscillations are not possible under the given heave conditions. The wake vorticity dynamics is presented for the different reduced frequencies, which show that the leading edge vortex dynamics is progressively more complex as the reduced frequency is increased from small values. For the airfoil oscillating in pitch, the airfoil is forced to oscillate about a large mean angle of attack corresponding to the stall regime. The unsteady moment on the blade is obtained at different reduced frequencies, and this is used to calculate the net energy transfer to the airfoil from the flow, which is found to be positive in all cases studied. This implies that stall flutter or self-induced oscillations are possible in the pitch mode, unlike in the heave case. The wake vorticity dynamics for this case is found to be relatively simple compared to that in heave. The results of the present simulations are broadly in agreement with earlier stall flutter studies at higher Reynolds numbers that show that stall flutter does not occur in the heave mode, but can occur in the pitch mode. The main difference in the present very low Reynolds number case appears to be the broader extent of the excitation region in the pitch mode compared to large Re cases studied earlier. region in the pitch mode compared to large Re cases studied earlier.