High-order essentially non-oscillatory (ENO) finite-difference schemes are applied to the two-and three-dimensional compressible Euler and Navier-Stokes equations. Practical issues, such as vectorization, efficiency of coding, cost comparison with other numerical methods and accuracy degeneracy effects, are discussed. Numerical examples are provided which are representative of computational problems of current interest in transition and turbulence physics. These require both non-oscillatory shock capturing and high resolution for detailed structures in the smooth regions and demonstrate the advantage of ENO schemes.
Aerospace Engineering (ABSTRACT)A new numerical procedure has been developed for the finite-volume solution of the Euler equations on unstructured, triangular meshes using a flux-difference split, upwind method. The procedure uses a dual mesh system to implement the finite-volume scheme using conserved variables stored at the vertices of the triangles. The vertices of the triangles are located approximately in the center of the dual mesh cells and conservation is enforced about each dual mesh finite-volume.Techniques are developed for implementing Roe's approximate Riemann solver on unstructured grids.Higher order accuracy is achieved by using MUSCL-differencing. MUSCL-differencing is implemented on an unstructured grid by interpolating the values stored at the vertices of triangular elements to find the value at the outermost point of the three-point MUSCL-differencing formula. Flow solutions are computed using a four-stage Runge-Kutta time integration. Convergence is accelerated using non-standard weighting of the Runge-Kutta stages, variable time-steps, residual smoothing and residual minimization. Applications and comparisons with structured grid solutions are made for a supersonic shock reflection problem, the supersonic flow over a blunt body, flow through a simple wedge inlet, and several AGARD 07 working group transonic airfoils. In general, the solutions computed by the upwind solver on the unstructured grids were as accurate as upwind solutions on a structured mesh.The blunt body solution, and some of the transonic airfoil solutions on the unstructured meshes, appeared to be less accurate than the structured mesh solutions. Fortuitously, the structured meshes used in these solutions tended to line up with the shock waves present in the flow-field. The upwind flux-differencing scheme captured the shock wave with greatest accuracy when it was applied normal to the discontinuity, as was done in these test cases.
Several patients with documented permanent sensorineural hearing losses secondary to the use of cordless telephones have been evaluated. In the interests of saving space and weight, these units have the ear receiver double as the ringing or bell device. The output of the bell on all of the units we have tested to date has been in the 140-dB range on the A scale. In each instance, the patient held the telephone against the ear when ringing occurred, and in three instances a loud extraneous crack was transmitted. Unlike regular cord-type telephones, these devices have no automatic gain control in the receiver circuit.
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