Shutian Deng

Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Mathematics



First Advisor

Chaoqun Liu


In this paper, direct numerical simulation (DNS) of flow transition over a flat plate at a free stream Mach number of 0.5 and a Reynolds number of 1000 based on the free stream velocity and inflow displacement thickness has been carried out. The time-dependent Navier-Stokes equations are solved directly by a third-order TVD Runge-Kutta method from Shu(1998). A sixth order central compact scheme from Lele (1992) that facilitates high resolution of the flow field is used for spatial discretization together with a sixth order implicit compact filter. To avoid possible non-physical wave reflection from the boundaries, the non-reflecting boundary conditions Jiang et al. (1999) are specified at the far field and the outflow boundaries. The inflow is specified by laminar flow profile with imposed eigenmodes of two-dimensional and three-dimensional Tollmien-Schlichting (T-S) waves and random noise. The parallel computation is accomplished through the Message Passing Interface (MPI) together with a domain decomposition approach. Computation is carried out currently in three different grids levels: 256x32x64, 640x64x60 and 1536x128x64 in the streamwise (x), spanwise (y), and wall normal (z) directions. In this paper, by integrating all these papers, a better view and more detail investigations about the back ground of the study, more details on different grid levels and more complete conclusions are documented. The DNS results show the mean flow properties, such as the skin friction coefficients and the mean velocity profile, wall shear linear law, log law in the turbulent region, as well as the spatial evolution of disturbance modes which agree very well with the theoretic and experimental results. Some of the structures appeared in the transition region are also studied. In addition, the statistics and spectrum analysis of the turbulence region, kinetic energy revolution and Reynolds stress are also shown in this paper. The spectra analysis shows that our resolution at the 1536x128x64 is adequate. All computational results are in good agreement with other reported work.


Mathematics | Physical Sciences and Mathematics


Degree granted by The University of Texas at Arlington

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