ISSN:0029-5639    

DOI:10.13182/NSE86-A17858

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractThe development and testing of alternative numerical methods and computational algorithms specifically designed for the vectorization of transport and diffusion computations on a Control Data Corporation (CDC) Cyber 205 vector computer are described. Two solution methods for the discrete ordinates approximation to the transport equation are summarized and compared. Factors of 4 to 7 reduction in run times for certain large transport problems were achieved on a Cyber 205 as compared with run times on a CDC-7600.The solution of tridiagonal systems of linear equations, central to several efficient numerical methods for multidimensional diffusion computations and essential for fluid flow and other physics and engineering problems, is also dealt with. Among the methods tested, a combined odd-even cyclic reduction and modified Cholesky factorization algorithm for solving linear symmetric positive definite tridiagonal systems is found to be the most effective for these systems on a Cyber 205. For large tridiagonal systems, computation with this algorithm is an order of magnitude faster on a Cyber 205 than computation with the best algorithm for tridiagonal systems on a CDC-7600.The above-mentioned algorithm for solving tridiagonal systems is also used as a basis for a new hyperline method for implementing the red-black cyclic Chebyshev iterative method to the solution of two-dimensional diffusion problems. The hyperline method is found to be competitive with other alternative options. This hyperline method has an attractive feature of being compatible with so-called concurrent iteration procedures whereby iterations n + 1,…, n + k, can be started before the completion of iteration n. This feature is very effective in balancing computations and data transfer requirements for very large diffusion problems. Consequently, the hyperline method is suitable for implementation for the solution of three-dimensional diffusion problems.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17859

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractFor the numerical solution of sparse systems of linear equations arising from the finite difference approximation of the multidimensional neutron diffusion equation, fast methods are needed. Effective algorithms for scalar computers may not be likewise suitable on vector computers.In the improved version (DIXY2) of the Karlsruhe two-dimensional neutron diffusion code for rectangular geometries, an incomplete Cholesky conjugate gradient (ICCG) algorithm has been combined with the originally implemented cyclically reduced four-line successive overrelaxation (CR4LSOR) inner iteration method. The combined procedure is automatically activated for slowly converging applications, thus leading to a drastic reduction of iterations as well as CPU times on a scalar computer. In a follow-up benchmark study, necessary modifications to ICCG and CR4LSOR for use on a vector computer were investigated.It was found that a modified preconditioning for the ICCG algorithm restricted to the block diagonal matrix is an effective method both on scalar and vector computers. With a splitting of the nine-band matrix in two triangular Cholesky matrices, necessary inversions are performed on a scalar machine by recursive forward and backward substitutions. On vector computers an additional factorization of the triangular matrices into four bidiagonal matrices enables Buneman reduction, and the recursive inversion is restricted to a small system. A similar strategy can be realized with CR4LSOR if the unvectorizable Gauss-Seidel iteration is replaced by Double Jacobi and Buneman techniques for a vector computer. Compared to single-line blocking over the original mesh, the cyclical four-line reduction of the DIXY inner iteration scheme reduces numbers of iterations and CPU times considerably.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17860

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractThe performance of a nonstationary iterative scheme for solving the large system of linear equations arising in neutron diffusion calculations is reported. The method is compared with successive overrelaxation and conjugate gradient methods. Practical aspects of its implementation on computers are considered.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17861

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractThe standard point kinetics equations and formally exact expressions for reactivity, prompt neutron lifetime, and effective delayed neutron fractions are derived from the matrix form of the nodal code QUANDRY. Perturbation theory expressions for reactivity based both on the standard quadratic-transverse-leakage form of QUANDRY and on the coarse-mesh finite difference (CMFD) form, made accurate by the use of discontinuity factors, are derived. With three-dimensional CMFD QUANDRY transient calculations taken as numerical standards, the accuracy of several standard point kinetics methods as well as the improved quasi-static method is tested. Results suggest that point kinetics methods are poor for rod ejection calculations, even if a precalculated table of rod worth versus position is used to infer the reactivity contribution of the moving rods. For transients not involving rod motion, the point kinetics equations are more accurate. Use of core-averaged (rather than node-dependent) temperature coefficients, however, can produce significant errors. The quasistatic scheme appears to yield acceptably accurate results but, for the tests run, consistently required more computing time than needed for the full three-dimensional solutions.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17862

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractA new method for solving the neutron diffusion equations in multiconnected regions with arbitrarily shaped boundaries has been developed by using a compound boundary-fitted coordinate transformation. In the compound boundary-fitted coordinate transformation, inner regions and an outer region in the physical plane are transformed by different coordinate systems. The neutron diffusion equations obtained by the coordinate transformation are solved in the rectangular coordinate system for the outer region, and in the cylindrical coordinate system for the inner regions, so that the boundary conditions are represented accurately and detailed calculations in a particular region can be performed without increasing the number of grid points in other regions.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17863

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractA new approach has been proposed to solve the transport equation for nonuniform lattices. The assumptions made permit transformation of the response matrix scheme into a diffusion-type equation and the specification of the boundary conditions of the cell problems to be solved. The new approach uses quantities that can be considered as a generalization of the diffusion coefficient.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17864

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractThe efficient use of nodal methods for three-dimensional two-group reactor calculations requires homogenization over large volumes or nodes. This homogenization removes the internal structure of the nodes. On the other hand, accurate pinwise power distributions are indispensable for light water reactor design. A homogenization and dehomogenization procedure called the simplified equivalence theory (SET) has been proposed, which allows the accurate and inexpensive determination of pinwise power distributions of fresh reactor cores. The SET procedure is extended to burnup and parameter dependencies. For the case of fuel assembly homogenization and dehomogenization, this extension is validated by a procedure that allows assessment of the accuracy of the method, referring exclusively to the spectral geometry of the assembly. For the validation of the equivalent reflector model, a nodal reactor test problem is set up which shows that this model is adequate to describe core/reflector interactions under burnup conditions.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17865

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractA dynamic grid adaptive method has been developed for use with the asymmetric weighted residual method. The method automatically adapts the number and position of the spatial mesh points as the solution of hyperbolic or parabolic vector partial differential equations progresses in time. The mesh selection algorithm is based on the minimization of the L2norm of the spatial discretization error. The method permits the accurate calculation of the evolution of inhomogeneities, like wave fronts, shock layers, and other sharp transitions, while generally using a coarse computational grid. The number of required mesh points is significantly reduced, relative to a fixed Eulerian grid. Since the mesh selection algorithm is computationally inexpensive, a corresponding reduction of computing time results.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17866

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor

摘要:

AbstractThe numerical calculation of critical two-phase flow in a convergent-divergent nozzle is complicated by a singularity of the fluid flow equations at the unknown critical point. A method of calculating critical state and its location without any additional assumptions is described. The critical state is identified by its mathematical properties: characteristics and solvability of linear systems with a singular matrix. Because the numerically estimable mathematical properties are the only necessary conditions for the existence of critical flow, some physical“compatibility criteria”(flow velocity equals model-consistent two-phase sonic velocity; critical flow is independent of downstream flow state variations) are used as substitutes for mathematically sufficient conditions. Numerical results are shown for the critical flow through LOBI nozzles and for the Super Moby Dick experiment. The two-phase flow is described by a model with equal phase velocities and thermodynamic nonequilibrium.

ISSN:0029-5639    

DOI:10.13182/NSE86-A17867

出版商:Taylor&Francis    

年代:1986

数据来源: Taylor