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Представлен вариант обратного метода характеристик (МОМХ), в алгоритм которого введен дополнительный дробный временной шаг, что позволяет повысить точность вычислений за счет более точной аппроксимации характеристик. Приведены расчетные формулы модифицированного метода для уравнений односкоростной модели газожидкостной смеси, с помощью которого рассчитаны одномерные, а также плоские тестовые задачи, имеющие автомодельные решения. При решении многомерных задач исходная система уравнений расщепляется на ряд одномерных подсистем, для расчета которых применяется обратный метод характеристик с дробным временным шагом. С использованием предложенного метода рассчитаны: одномерная задача распада произвольного разрыва в дисперсной среде; двумерная задача взаимодействия однородного газожидкостного потока с препятствием с присоединенным ударным скачком, а также течение с центрированной волной разрежения. Результаты численных расчетов этих задач сопоставлены с автомодельными решениями и отмечено их удовлетворительное совпадение. На примере задачи Римана с ударным скачком приведено сравнение с рядом консервативных, неконсервативных первого и повышенного порядков точности схем, из которого, в частности, следует, что представленный метод расчета вполне конкурентоспособен. Несмотря на то что применение МОМХ требует в разы больших временных затрат по сравнению с оригинальным обратным методом характеристик (ОМХ), вычисления можно проводить с увеличенным временным шагом и в ряде случаев получать более точные результаты. Отмечено, что метод с дробным временным шагом имеет преимущества в случаях, когда характеристики системы криволинейные. По этой причине для уравнений Эйлера целесообразно использовать ОМХ вместо МОМХ, поскольку в этом случае характеристики в пределах временного шага мало отличаются от прямых линий.
8A hybrid spectral nodal method for multigroup X,Y-geometry discrete ordinates eigenvalue problems
A hybrid spectral nodal method for multigroup X,Y-geometry discrete ordinates eigenvalue problems
6Analytical spatial reconstruction scheme for the coarse-mesh solutions generated by the constant spectral nodal method for monoenergetic discrete ordinates transport calculations in X,Y geometry fission–chain reacting systems
Analytical spatial reconstruction scheme for the coarse-mesh solutions generated by the constant spectral nodal method for monoenergetic discrete ordinates transport calculations in X,Y geometry fission–chain reacting systems
Read more44Nodal diffusion methods and lattice physics data in LWR analyses: Understanding numerous subtle details
Nodal diffusion methods and lattice physics data in LWR analyses: Understanding numerous subtle details
12A finite element method for diffusion theory embracing nodal and difference methods
A finite element method for diffusion theory embracing nodal and difference methods
28The relation between finite element methods and nodal methods in transport theory
The relation between finite element methods and nodal methods in transport theory
1A high-order nodal discontinuous Galerkin method for simulation of three-dimensional non-cavitating/cavitating flows
A high-order nodal discontinuous Galerkin method for simulation of three-dimensional non-cavitating/cavitating flows
8A high-order nodal discontinuous Galerkin method for solution of compressible non-cavitating and cavitating flows
A high-order nodal discontinuous Galerkin method for solution of compressible non-cavitating and cavitating flows
An Innovative Reactor Analysis Methodology Based on a Quasidiffusion Nodal Core Model. Nuclear Energy Research Initiative (NERI) Program. Quarterly Technical Progress Report, July 1 - September 30, 2000
Status Summary of Nuclear Energy Research Initiative (NERI) Tasks: Task 1--The development of the following methods in ID slab geometry: (1) Homogenization and definition of discontinuity factors, (2) Group constants functionalization using assembly transport solution of multigroup eigenvalue problem with albedo boundary conditions, and (3) Solving coarse-mesh effective few-group 1D QD moment equations using tables of data parametrized with respect to the ratio {rvec n} {center_dot} {rvec {tilde J}{sup G}}/{tilde {phi}{sup G}} on boundaries. Task 2--Development of a numerical method for solving the 2D few-group moment QD equations: (1) Development of a nodal discretization method for 2D moment QD equations, and (2) Development of an efficient iteration method for solving the system of equations of the nodal discretization method for 2D moment QD equations. Task 3--The development of the following methods in 2D X-Y geometry: (1) homogenization and definition of discontinuity factors, (2) group constants functionalization using assembly transport solution of multigroup eigenvalue problem with albedo boundary conditions, and (3) solving coarse-mesh effective few-group QD moment equations using tables of data parametrized with respect to the ratio {rvec n} {center_dot} {rvec {tilde J}{sup G}}/{tilde {phi}{sup G}} on boundaries. Task 4--Development of a numerical method for solving the few-group moment QD equations in 3D geometry: (1) Development of a nodal method for discretization of 3D moment QD equations, and (2) Development of an efficient iteration method for solving the system of nodal discretized equations of moment QD equations in 3D geometry.
Read more20A response matrix spectral nodal method for energy multigroup X,Y-geometry discrete ordinates problems in non-multiplying media
A response matrix spectral nodal method for energy multigroup X,Y-geometry discrete ordinates problems in non-multiplying media
Read moreVariational nodal transport methods for hexagonal and three-dimensional geometries. Final report
The properties of the variational nodal method for neutron transport calculations are investigated. The method is generalized for three-dimensional multigroup criticality problems in both hexagonal-z and Cartesian geometries. The method is implemented as part of the Argonne National Laboratory Code DIF3D, and applied to a series of benchmark reactor calculations. Variational nodal methods are compared of nodal transport methods based on both interface-current and discrete ordinate approximations. Model problems are used to examine the effect of running each of the three classes of nodal transport methods on computers with massively parallel architectures.
Read more2Third order nodal finite element methods with transverse and reduced integration for elliptic problems
Third order nodal finite element methods with transverse and reduced integration for elliptic problems
14General nodal expansion method for multi-dimensional steady and transient convection–diffusion equation
General nodal expansion method for multi-dimensional steady and transient convection–diffusion equation
Numerical investigation of nucleation and coagulation processes and the influence on nanoparticle size distribution based on nodal method
The individual homogeneous nucleation, heterogeneous condensation, coagulation and the complete process of them are investigated numerically based on the nodal method. Results of nanoparticle size distribution (NPSD) due to above processes are also presented and discussed in this paper. At a given temperature, nanoparticles are first formed through homogeneous nucleation process. Then heterogeneous condensation takes place, and NPSD changes due to the interaction between nanoparticles and monomers. Finally nanoparticles undergo coagulation, which is the dominant factor to determine NPSD when temperature is relatively low. After all these processes, NPSD tends to be log-normal.
Read more1An adaptive p-refinement strategy applied to nodal expansion method in 3D Cartesian geometry
An adaptive p-refinement strategy applied to nodal expansion method in 3D Cartesian geometry
Free Vibrations of Cylindrical Shells by The Nodal Line Finite Difference Method-Part-I Theory.(Dept.C)
In this paper, the nodal line finite difference method (NLFDM) is extended to the analysis of a thin circular cylindrical shell, as shown in Fig. 1, undergoing free vibrations [1]. The material of the circular cylindrical shell is assumed to be linear elastic isotropic. The complexity of a theoretical analysis of a vibration problem depends largely on the number of degrees of freedom of the structural system in question. Since a thin circular cylindrical shell is a continuous system it has an infinite number of degrees of freedom. The NLFDM [10] transforms this continuous system into a system having a finite number of degrees of freedom. While carrying out the dynamic (or static) analysis by the NLFDM, the number of degrees of freedom depends on the number of the used nodal lines. The natural frequencies and modes are treated in more detail because they are basic to understanding the dynamic response under any kind of excitation. It will be shown that the number of natural frequencies and that of normal modes, for axial wave number different from zero, are each equal to three times the number of nodal lines used. The orthogonality relationships of the normal modes obtained by the nodal line finite difference method are also included. It should be remarked that these relationships are slightly different from those obtained by the finite element method; in fact the overall matrix of coefficients replaces the stiffness matrix, and any two different modes are orthogonal with resp ect to the unit matrix instead of the mass matrix.
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