Maria Oliveira

DNS for Late Stage Structure of Flow Transition on a Flat-Plate Boundary Layer

Direct numerical simulation of a spatially evolution flat-plate boundary layer transition process at free stream Mach number 0.5 is performed. The inflow is specified by laminar flow profile with imposed eigenmodes of two-dimensional and three dimensional Tollmien-Schlichting (T-S) waves. The parallel computation is accomplished through the Message Passing Interface (MPI) together with domain decomposition in the streamwise direction. H-type transition scenario is represented in the result of numerical simulation. Vortical structures formed by TS-waves and events at late stages of transition in wall boundary shear layers are investigated. Λ - (horseshoe-) vortices, Λ -shaped high-shear layers, and trains of ring-like ( Ω -, hairpin-) vortices are studied. These vortical structures are similar with which has been found in K-type transition scenario. The purpose of this DNS study is to understand the physics of the late transition stages. Many remaining questions related to the late stages of flow transition have been answered by this DNS study. Nomenclature ∞ M = Mach number Re = Reynolds number in δ = inflow displacement thickness w T = wall temperature

A new shock/discontinuity detector

A new effective shock/discontinuity detector has been developed in this work. The detector has two steps. The first step is to check the ratio of the truncation errors on the coarse and fine grids, and the second step is to check the local ratio of the left- and right-hand slopes. The currently popular shock/discontinuity detectors such as Hartens, Jamesons and WENO can detect shock, but mistake high-frequency waves and critical points as shock and then damp the physically important high-frequency waves. Preliminary results show that the new shock/discontinuity detector is very delicate and can detect all shocks including strong, weak and oblique shocks or discontinuity in function and first-, second- and third-order derivatives without artificial case-related constants, but never mistake high-frequency waves and critical points or expansion waves as shock. This will overcome the bottleneck problem with numerical simulation for the shock–boundary layer interaction, shock–acoustic interaction, image process, porous media flow, multiple phase flow, detonation wave, and anywhere the high-frequency waves are important, but discontinuity exists and is mixed with high-frequency waves. After detecting the shock, we can then use one-side high-order scheme for shocks and high-order central compact scheme for the smooth parts if the shock is appropriately located. Then a high-order universal subroutine for the finite difference method is developed, which can be used for any finite difference code for accurate numerical derivatives.

Modified Weighted Compact Scheme for Shock-Boundary Layer Interaction and Double Cone

The critical problem of CFD is perhaps an accurate approximation of derivatives for a given discrete data set. Based on our previous work on the weighted compact scheme (WCS), a modified weighted compact scheme (MWCS) has been developed. Similar to WENO, three high order candidates, left, right, and central, are constructed by Hermite polynomials. According to the smoothness, three weights are derived and assigned to each candidate. The weights will lead the scheme to be bias when approaching the shock or other discontinuities but quickly becomes central, compact, and of high order just off the shock. Therefore, the new scheme can get a sharp shock without oscillation, but keep central, compact and of high resolution in the smooth area. This feature is particularly important to numerical simulation of the shock-boundary layer interaction, where both shock and small eddies are important. The new scheme has three compact candidate stencils, 2 1 0 , , E E

Universal High Order Subroutine with New Shock Detector for Shock Boundary Layer Interaction

The goal of this work is to develop a new universal high order subroutine for shock boundary layer interaction. First, an effective shock/discontinuity detector has been developed.The detector has two steps.The first step is to check the ratio of the truncation errors on the coarse and fine grids and the second step is to check the local ratio of the left and right slopes. The currently popular shock/discontinuity detectors can detect shock, but mistake high frequency waves and critical points as shock and then damp the physically important high frequency waves.Preliminary results show the new shock/discontinuity detector is very delicate and can detect all shocks including strong, weak and oblique shocks or discontinuity in function and the first, second, and third order derivatives without artificial constants, but never mistake high frequency waves and critical points, expansion waves as shock. This will overcome the bottle neck problem with numerical simulation for the shock-boundary layer interaction, shock-acoustic interaction, image process, porous media flow, multiple phase flow and anywhere the high frequency waves are important, but discontinuity exists and is mixed with high frequency waves. After detecting the shock we can then use one side high order scheme for shocks and high order central compact scheme for the rest if the shock is appropriately located. Then a high order universal subroutine for finite difference method is developed which can be used for any finite difference code for accurate numerical derivatives.

New shock detector for shock-boundary layer interaction

Standard compact scheme or upwind compact scheme have high order accuracy and high resolution, but cannot capture the shock which is a discontinuity. This work developed a modified compact scheme by an effective shock detector to block compact scheme to cross the shock, a control function, and an adaptive scheme which uses some WENO flux near the shock. The new scheme makes the original compact scheme able to capture the shock sharper than WENO and, more important, keep high order accuracy and high resolution in the smooth area which is particularly important for shock boundary layer interaction and shock acoustic interaction. The scheme is robust and has no case-related coefficients.

High-order compact scheme for boundary points

In this paper, we introduce a new high-order scheme for boundary points when calculating the derivative of smooth functions by compact scheme. The primitive function reconstruction method of ENO schemes is applied to obtain the conservative form of the compact scheme. Equations for approximating the derivatives around the boundary points 1 and N are determined. For the Neumann (and mixed) boundary conditions, high-order equations are derived to determine the values of the function at the boundary points, 1 and N, before the primitive function reconstruction method is applied. We construct a subroutine that can be used with Dirichlet, Neumann, or mixed boundary conditions. Numerical tests are presented to demonstrate the capabilities of this new scheme, and a comparison to the lower-order boundary scheme shows its advantages.

Truncation error, dissipation and dispersion terms of fifth order WENO and of WCS for 1D conservation law

In this paper, a derivation and a comparison of the truncation errors and the dissipation and dispersion terms of the fifth-order weighted essentially non-oscillatory scheme and of the weighted compact scheme are presented. The schemes are compared for smooth functions (by Fourier analysis), and near a shock.

Weighted compact schemes for shock/boundary layer interaction

In this paper, we introduce a new type of weighted, finite-difference schemes. The basic idea comes from the compact schemes discussed in [le le92] paper and the weighted compact schemes proposed in [jiang01] paper. The purpose of this new scheme is to achieve spectral-like resolution and high order of accuracy in smooth regions and to keep the ability to capture shocks without sacrificing the order of accuracy too much. This is really a hybrid scheme that the flux of the conservative Navier-Stokes equations is given by weighted compact scheme (WCS) but with some components from 5th order WENO ([jiang96]). The former gives sharp shock and high resolution, but the later provides necessary dissipation to avoid non-physical oscillations. In the paper, a sixth-order weighted compact scheme and corresponding 5th order WENO are combined following this basic idea. Numerical tests show that the new scheme has improved performance for the problems of two-dimensional shock/boundary layer interaction including test cases with incident shock and double cones. The scheme is especially appropriate for the problems of shock/boundary layer, shock/vertex or shock/turbulence interaction.

Implicit LES for Shock/Blunt Body Interaction

The numerical simulation of the three-dimensional flow upwind of a vertical cylinder over a flat plate is achieved with a parallel LES code which is called DNSUTA Version III. The preliminary computational results with a coarse grid find that the flow structure is similar to experimental observations. The bow shock is very clear, and a separation shock is formed ( Λ-structure). Inside the separation region, there is a supersonic zone clearly visible. We also observe a high pressure zone near the cylinder wall, where the separation shock meets the bow shock. We observe high temperatures at the cylinder surface, as detected in experiments. The streamlines show the separation zone and the vortices are clearly outlined. Also, the root vortex is clearly shown at the base of the cylinder. With a finer grid which we plan to use, it will be very likely to observe more details of the structure for shock/blunt body interaction.

High Order Weighted Compact Scheme for Shock/Boundary Layer Interaction

In this paper, we introduce a new type of weighted, finite-difference schemes. The basic idea comes from the compact schemes discussed in Lele’s paper and the weighted compact schemes proposed in Jiang’s paper. The purpose of this new scheme is to achieve spectrallike resolution and high order of accuracy in smooth regions and to keep the ability to capture shocks without sacrificing the order of accuracy too much. This is really a hybrid scheme that the flux of the conservative Navier-Stokes equations is given by weighted compact scheme (WCS) but with some components from 5th order WENO. The former gives sharp shock and high resolution, but the later provides necessary dissipation to avoid non-physical oscillations. In the paper, a sixth-order weighted compact scheme and corresponding 5th order WENO are combined following this basic idea. Numerical tests show that the new scheme has improved performance for the problems of two-dimensional shock/boundary layer interaction including test cases with incident shock and double cones. The scheme is especially appropriate for the problems of shock/boundary layer, shock/vertex or shock/turbulence interaction.