Fortran

We present a stable and efficient Fortran implementation of polynomial interpolation at the Padua points on the square [ − 1,1] 2 . These points are unisolvent and their Lebesgue constant has minimal order of growth (log square of the degree). The algorithm is based on the representation of the Lagrange interpolation formula in a suitable orthogonal basis, and takes advantage of a new matrix formulation together with the machine-specific optimized BLAS subroutine for the matrix-matrix product. Extension to interpolation on rectangles, triangles and ellipses is also described.

A numerical study has been conducted to investigate the fluid flow and heat transfer of an air-cooled metal foam heat exchanger under the high speed laminar jet confined by two parallel walls for which the range of the Reynolds number is 600–1000. Two independent numerical solvers were used and cross-validated being a FORTRAN code and the commercially available software CFD-ACE. The effects of local thermal non-equilibrium, thermal dispersion, porosity, and pore density on the heat transfer augmentation are examined for different Reynolds numbers. Application of energy flux vectors, for convection visualization, is also illustrated for a more comprehensive analysis of the problem. Finally, the performance of the metal foam heat exchanger is compared to that of conventional finned design. It is observed that the heat removal rate can be greatly improved at almost no excess cost.

The numerical methods employed in the solution of many scientific computing problems require the computation of derivatives of a function~: R “+ Rm. ADIFOR(Automatic Differentiation In FORtran) is a source transformation tool that accepts Fortran 77 code for ...

This project work report provides a full solution of simplified Navier Stokes equations for The Incompressible Couette Problem. The well known analytical solution to the problem of incompressible couette is compared with a numerical solution. In that paper, I will provide a full solution with simple C code instead of MatLab or Fortran codes, which are known. For discrete problem formulation, implicit Crank-Nicolson method was used. Finally, the system of equation (tridiagonal) is solved with both Thomas and simple Gauss Method. Results of both methods are compared.

Here, we report the efficient and feasible analytical method for the generalized Bloch–Gruneisen law in association with Debye temperature and various temperatures range in terms of incomplete gamma function. In addition, our results are in agreement with previous reports as shown in this letter. Bloch–Gruneisen function describes the contribution of electron–phonon interaction to the results of temperature dependence behavior of resistivity for integer and noninteger values of index m. In conclusion, the algorithm is constructed in Fortran 90 language for replicate the variation of temperature dependence of resistivity for pristine MgB2 sample. Moreover, the comparison of numerical results with the proposed method reveals the validity and precision of the method.