Two-dimensional Non-periodic Steady Flow Of Harmonic Analysis Method

In this dissertation, a highly efficient way of modeling periodic unsteady flow field is studied. As already existent mature method of solving the problem mentioned above, dual time stepping, which is developed by Jameson, can use the very effective way of accelerating convergence, the so called multigrid method. But that is not enough and recently a very hopeful new way called harmonic balance method which can do the job in an incredible efficient way comes up.When the unsteady flow is temporally periodic, the flow variables (always the conservation variables) can be expanded as a Fourier series (but with finite terms). When take these expressions into the flow control equations, the problem can be analyzed in frequency domain. Then the calculation can be carried out either directly in this same domain or in the time domain. Either way calls the attention of doing the math on flux terms. The research showed in this thesis take the time domain path. This author argued that the code can be easily obtained from the former time domain program. The main aspects of this dissertation are as follows:(1). To verifies the outstanding performance of harmonic balance method, code for dual time stepping was also made by this author. For the unsteadiness of the flow is caused by the motion of a certain body (such as airfoil), a still reference system and mobile mesh method is applied. Also this dual time stepping method takes the advantage of multigrid technique.(2).Within harmonic balance method, if computations are carried out in the time domain, the detailed process are characterized in this way, all the instant flow fields are coupled to form the approximate time derivative term with spectral operator. Also it can be easily noticed that all the instant flow fields are marched forward in a kind of neck and neck way with respect to fictitious time. DFT and IDFT are used during the calculation of approximate time derivative term. To facilitate convergence, multigrid technique is also utilized.Results from modeling the airfoil pitching problem show that, while the use convergence accelerating technique being equal (for instance, a 3 level W cycle Multigrid method is used in both means), the capability of the computer being equal, the compiling and running environment is kept the same, acceptable results can be gained from the harmonic balance method with just quite few terms retained in the...