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  • FLUID MECHANICS AND HEAT TRANSFER  (9)
  • 2010-2014
  • 1980-1984  (9)
  • 1
    Publication Date: 2011-08-18
    Description: A set of nonlinear partial differential equations suitable for the description of a class of turbulent three-dimensional flow fields in select geometries is identified. On the basis of the concept of enforcing a penalty constraint to ensure accurate accounting of ordering effects, a finite element numerical solution algorithm is established for the equation set and the theoretical aspects of accuracy, convergence and stability are identified and quantized. Hypermatrix constructions are used to formulate the reduction of the computational aspects of the theory to practice. The robustness of the algorithm, and the computer program embodiment, have been verified for pertinent flow configurations.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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  • 2
    Publication Date: 2011-08-18
    Description: The formal derivation of the three-dimensional parabolic Navier-Stokes equations for subsonic turbulent flow is reviewed. A penalty finite element algorithm is established for numerical solution of the sixteen dependent variable system. Key numerical results are summarized documenting applications in various problem definitions.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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  • 3
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    Publication Date: 2011-08-18
    Description: Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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  • 4
    Publication Date: 2019-06-28
    Description: A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: NASA-CR-172256 , NAS 1.26:172256 , COMCO-83-TR-2.1
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  • 5
    Publication Date: 2019-06-28
    Description: The Galerkin-weighted residuals formulation is employed to derive an implicit finite element solution algorithm for a generally non-linear initial-boundary value problem. Solution accuracy and convergence with discretization refinement are quantized in several error norms, for the non-linear parabolic partial differential equation system governing laminar boundary layer flow, using linear, quadratic and cubic functions. Richardson extrapolation is used to isolate integration truncation error in all norms, and Newton iteration is employed for all equation solutions performed in double-precision. The mathematical theory supporting accuracy and convergence concepts for linear elliptic equations appears extensible to the non-linear equations characteristic of laminar boundary layer flow.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Computers and Fluids; 9; Mar. 198
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  • 6
    Publication Date: 2019-06-28
    Description: An order-of-magnitude analysis of the subsonic three dimensional steady time averaged Navier-Stokes equations, for semibounded aerodynamic juncture geometries, yields the parabolic Navier-Stokes simplification. The numerical solution of the resultant pressure Poisson equation is cast into complementary and particular parts, yielding an iterative interaction algorithm with an exterior three dimensional potential flow solution. A parabolic transverse momentum equation set is constructed, wherein robust enforcement of first order continuity effects is accomplished using a penalty differential constraint concept within a finite element solution algorithm. A Reynolds stress constitutive equation, with low turbulence Reynolds number wall functions, is employed for closure, using parabolic forms of the two-equation turbulent kinetic energy-dissipation equation system. Numerical results document accuracy, convergence, and utility of the developed finite element algorithm, and the CMC:3DPNS computer code applied to an idealized wing-body juncture region. Additional results document accuracy aspects of the algorithm turbulence closure model.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: NASA-CR-3645 , NAS 1.26:3645 , COMCO-81TR-2.1
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  • 7
    Publication Date: 2019-06-28
    Description: The Galerkin-Weighted Residuals formulation is employed to derive an implicit finite element solution algorithm for the nonlinear parabolic partial differential equation system governing turbulent boundary layer flow. Solution accuracy and convergence with discretization refinement are quantized in several error norms using linear and quadratic basis functions. Richardson extrapolation is used to isolate integration truncation error in all norms, and Newton iteration is employed for all equation solutions performed in double-precision. The mathematical theory supporting accuracy and convergence concepts for linear elliptic equations appears extensible to the nonlinear equations characteristic of turbulent boundary layer flow.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Computer Methods in Applied Mechanics and Engineering; 28; Aug. 198
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  • 8
    Publication Date: 2019-06-28
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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  • 9
    Publication Date: 2019-07-13
    Description: The thin-layer simplification of the two-dimensional Navier-Stokes equations for steady viscous flow are developed using an order of magnitude analysis. A space marching finite element solution algorithm is developed, wherein the first order continuity effects are enforced as a penalty function differential constraint. Numerical results are presented to document accuracy and convergence features of the numerical solution algorithm.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Penalty-finite element methods in mechanics; Winter Annual Meeting; Nov 14, 1982 - Nov 19, 1982; Phoenix, AZ
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