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Table 1: The governing PDE apos;s for incompressible ow with heat transfer are shown in dimensionless form, including the Navier-Stokes equations with the Boussinesq approximation, the continuity equation, and a heat balance. Momentum
2000
"... In PAGE 5: ... In addition, a heat equation with convective and conduction terms is solved. The equations are shown in Table1 and include the time dependent terms, which are important for the formulation of the stability (eigenvalue) calcu- lation.The computational domain is discretized using a mesh of 94656 hexehe- dral elements, which corresponds to 100043 nodes.... ..."
Cited by 13
Table 1. Measured execution time and processing rate of the Navier-Stokes subprograms for the 128 x 128 problem on the MPP. I Subprogram I Execution I Percentage of I Processing I
1988
"... In PAGE 16: ...able 11. Measured execution times (in machine cycles) of the elementary operations on the MPP. Addition I Multiplication I Division I One step shift I k step shift 965 I 811 I 1225 1 168 I 136+32k . Table1 11 contains the operation counts per grid point for the Navier-Stokes subprograms on the MPP using the cyclic elimination algorithm for solving the tridiagonal systems. The arithmetic operations are counted in this table the way they were implemented; i.... ..."
Cited by 3
Table 4. Maximum Errors of the Pressure Function and Velocity Vector of Navier-Stokes Equations
1997
"... In PAGE 4: ... It should be noted that as the weak form of the boundary conditions for this problem involve second order derivatives of the stream function, a high order approximation of the stream function is necessary. Refer to Table4 for the accuracy of the pressure function approximations by the standard linear nite element method. Let us now introduce the bivariate spline space to be used to approximate the... In PAGE 42: ...avier-Stokes equations (1.1), we calculate the right-hand side function f. Using the f and the boundary values of the arti cial velocity over the boundary of the L-shape domain, we compute the numerical solutions by our MATLAB programs and then compute the error against the arti cial solution. In Table4 , we list the maximum error, based on 30401 points equally spaced over the L-shape domain which is triangulated as shown in Figure 1 and is re ned two times. In Table 4, the Reynolds number is 100.... ..."
Cited by 2
Table 3. Redesign of Boeing 747 at Mach .85 and CL:45using the Reynolds Averaged Navier-Stokes equations with Baldwin-Lomax turbulent model.
"... In PAGE 8: ... After 60 design cycles (total compu- tational cost of ow and gradient calculation is equivalent to 12 ow solutions), improvement in both drag and structural weight can be achieved. Table3 shows this improvement. Table 3.... ..."
Table 3: First-Order Doppler-Factored STAP on a single node of IBM SP2 and on a single node of SGI/Cray T3E
"... In PAGE 39: ...Results for First-Order Doppler-Factored STAP A data cube of size 16 (number of channels) 64 (PRI apos;s) 480 (range gates) was used as input for First-Order Doppler-Factored STAP. The sequential execution time of each task in each stage running on a single node of IBM SP2 and a single node of SGI/Cray T3E, and the number of tasks in each stage are shown in Table3 . Library routines (IBM essl library and LAPACK) were used for implementing the computational kernels (FFT, QRD, etc.... ..."
Table 1: Qualitative solution behavior of full Navier-Stokes equations, in a single coordinate direction, + means solution increase, ? solution decrease.
"... In PAGE 8: ... Finally, the double root (!x)5;6 implies a solution behavior which is exactly the opposite of that of (!x)3;4. In Table1 , the solution behavior in x-direction is summarized. The minus signs de ne solution decrease and the plus signs increase.... In PAGE 8: ...n x-direction is summarized. The minus signs de ne solution decrease and the plus signs increase. Because of the similarity of equation (2.7) with respect to !x; !y and !z, for the y- and z-directions, the tables corresponding to Table1 are similar. (The tables for the y- and z-direction can be directly obtained from Table 1 by replacing x; u; (!x)1?6 by y; v; (!y)1;:::;6 and z; w; (!z)1;:::;6, respectively.... In PAGE 8: ...7) with respect to !x; !y and !z, for the y- and z-directions, the tables corresponding to Table 1 are similar. (The tables for the y- and z-direction can be directly obtained from Table1 by replacing x; u; (!x)1?6 by y; v; (!y)1;:::;6 and z; w; (!z)1;:::;6, respectively.)... In PAGE 8: ...Table 1: Qualitative solution behavior of full Navier-Stokes equations, in a single coordinate direction, + means solution increase, ? solution decrease. For each of the four possible (x; u)-cases in Table1 , three exponentially growing solution modes appear (three plus signs per column). The same holds for the y- and z-direction.... ..."
Table 2: Qualitative solution behavior of reduced Navier-Stokes equations, in mainstream direction, + means solution increase, ? solution decrease.
Table 2. Comparison of pass rates of multipath fading distributions using full band
"... In PAGE 3: ... Tables below show, how different CDFs fit to the data. Table2 depicts all of the measurement environments from LOS to NLOS2 (c.f.... ..."
Table 5: The error in the reduced basis solution of the Navier-Stokes problem on a single-block domain. Results when we use empirical interpolation, and the polynomial degree N = 34.
"... In PAGE 14: ...tate solution. In this way we find seven basis function, and a reference solution. The convergence of the reduced basis method is presented in Table 4. In the last computations we have included the empirical interpolation, and we see from Table5 that the convergence is still very good.... ..."
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