Modified Block Newton method for the lambda modes problem

[EN] To study the behaviour of nuclear power reactors it is necessary to solve the time dependent neutron diffusion equation using either a rectangular mesh for PWR and BWR reactors or a hexagonal mesh for VVER reactors. This problem can be solved by means of a modal method, which uses a set of dominant modes to expand the neutron flux. For the transient calculations using the modal method with a moderate number of modes, these modes must be updated each time step to maintain the accuracy of the solution. The updating modes process is also interesting to study perturbed configurations of a reactor. A Modified Block Newton method is studied to update the modes. The performance of the Newton method has been tested for a steady state perturbation analysis of two 2D hexagonal reactors, a perturbed configuration of the IAEA PWR 3D reactor and two configurations associated with a boron dilution transient in a BWR reactor.This work has been partially supported by the Spanish Ministerio de Educación y Ciencia under projects ENE2008-02669 and MTM2007-64477-AR07, the Generalitat Valenciana under project ACOMP/2009/058, and the Universidad Politécnica de Valencia under project PAID-05-09-4285.González Pintor, S.; Ginestar Peiro, D.; Verdú Martín, GJ. (2013). Modified Block Newton method for the lambda modes problem. Nuclear Engineering and Design. 259:230-239. https://doi.org/10.1016/j.nucengdes.2011.06.045S23023925

Steady-state analysis techniques for coupled device and circuit simulation

The focus of this work is on the steady-state analysis of RE circuits using a coupled device and circuit simulator. Efficient coupling algorithms for both the time-domain shooting method and the frequency-domain harmonic balance method have been developed. A modified Newton shooting method considerably improves the efficiency and reliability of the time-domain analysis. Three different implementation approaches of the harmonic balance method for coupled device and circuit simulation are investigated and implemented. These include the quasi-static, non-quasi-static, and modified-Volterra-series approaches. Comparisons of simulation and performance results identify the strengths and weakness of these approaches in terms of accuracy and efficiency

Control and Limit Enforcements for VSC Multi-Terminal HVDC in Newton Power Flow

This paper proposes a novel method to automatically enforce controls and limits for Voltage Source Converter (VSC) based multi-terminal HVDC in the Newton power flow iteration process. A general VSC MT-HVDC model with primary PQ or PV control and secondary voltage control is formulated. Both the dependent and independent variables are included in the propose formulation so that the algebraic variables of the VSC MT-HVDC are adjusted simultaneously. The proposed method also maintains the number of equations and the dimension of the Jacobian matrix unchanged so that, when a limit is reached and a control is released, the Jacobian needs no re-factorization. Simulations on the IEEE 14-bus and Polish 9241-bus systems are performed to demonstrate the effectiveness of the method.Comment: IEEE PES General Meeting 201

Analysis of a parallelized nonlinear elliptic boundary value problem solver with application to reacting flows

A parallelized finite difference code based on the Newton method for systems of nonlinear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters is derived for algorithms based on stripwise and boxwise decompositions of the domain and a one-to-one assignment of the strip or box subdomains to processors. The sensitivity of the cost functions to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of nineteen equations with very expensive function evaluations. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedup of O(n), where n is mesh resolution in one direction, for reasonable n

Bubble simulations with an interface tracking technique based on a partitioned fluid-structure interaction algorithm

Numerical techniques frequently used for the simulation of one bubble can be classified as interface tracking techniques and interface capturing techniques. Most of these techniques calculate both the flow around the bubble and the shape of the interface between the gas and the liquid with one code. In this paper, a rising axisymmetric bubble is simulated with an interface tracking technique that uses separate codes to determine the position of the gas-liquid interface and to calculate the flow around the bubble. The grid converged results correspond well with experimental data. The gas-liquid interface is conceived as a zero-mass, zero-thickness structure whose position is determined by the liquid forces, a uniform gas pressure and surface tension. Iterations between the two codes are necessary to obtain the coupled solution of both problems and these iterations are stabilized with a fluid-structure interaction (FSI) algorithm. The flow around the bubble is calculated on a moving mesh in a reference frame that rises at the same speed as the bubble. The flow solver first updates the mesh throughout the liquid domain given a position of the gas-liquid interface and then calculates the flow around the bubble. It is considered as a black box with the position of the gas-liquid interface as input and the liquid forces on the interface as output. During the iterations, a reduced-order model of the flow solver is generated from the inputs and outputs of the solver. The solver that calculates the interface position uses this model to adapt the liquid forces on the gas-liquid interface during the calculation of the interface position

Stabilization of Unstable Procedures: The Recursive Projection Method

Fixed-point iterative procedures for solving nonlinear parameter dependent problems can converge for some interval of parameter values and diverge as the parameter changes. The Recursive Projection Method (RPM), which stabilizes such procedures by computing a projection onto the unstable subspace is presented. On this subspace a Newton or special Newton iteration is performed, and the fixed-point iteration is used on the complement. As continuation in the parameter proceeds, the projection is efficiently updated, possibly increasing or decreasing the dimension of the unstable subspace. The method is extremely effective when the dimension of the unstable subspace is small compared to the dimension of the system. Convergence proofs are given and pseudo-arclength continuation on the unstable subspace is introduced to allow continuation past folds. Examples are presented for an important application of the RPM in which a “black-box” time integration scheme is stabilized, enabling it to compute unstable steady states. The RPM can also be used to accelerate iterative procedures when slow convergence is due to a few slowly decaying modes