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This paper proposes an efficient segregated solution procedure for the two-dimensional incompressible fluid flow on unstructured grids. The new algorithm is called SIMPLERR (SIMPLERR-revised algorithm). It includes an inner iterative process that consists of a pressure equation solution and an explicit velocity correction, and then, the pressure field is obtained by another solving process for the pressure equation. The features and advantages of the SIMPLERR algorithm are demonstrated by solving a benchmark flow problem, and the results indicate that the SIMPLERR algorithm can maintain a strong stability as the IDEAL algorithm and can converge faster than the SIMPLER algorithm or even than the IDEAL algorithm. The advantage of the SIMPLERR algorithm is especially evident for high-Re and fine-mesh fluid flow cases, where the SIMPLERR algorithm and the IDEAL algorithm can obtain a convergence result but the SIMPLER algorithm cannot. The SIMPLERR algorithm is about two times faster than the IDEAL al...

In this paper, we are concerned with maximum flow problems with non-zero lower bounds. The common approach to this problem is transforming the network into a bigger one with zero lower bounds, whose optimal solution yields a feasible solution to the original problem and then using one of the established methods for maximum flow problems with little to no modifications. Expanding upon the labelling techniques of Goldfarb and Hao we show that a variant of the monotonic build-up simplex algorithm runs in strongly polynomial time on the original network. The main characteristic of the MBU algorithm is that starting from an arbitrary basis solution it decreases the number of infeasible variables monotonically, without letting any feasible variables turn infeasible in the process. We show that this algorithm terminates after at most pivots which makes it the first strongly polynomial pivot algorithm that solves the problem without transforming the network.

The author introduces a minimum cost maximum flows (MCMF) routing algorithm that allows the construction of a multicast tree that incorporates both static and dynamic nodes. The key idea of the algorithm is, first, finding the least delay path of the partial static tree (PST) from a source node to a set of static receivers, by using the ratio of "delay/number of flows" as cost function; and second, adding the dynamic nodes to the constructed PST, one by one, according to their arrival order, by minimizing the ratio "delay/number of flows." According to the presented simulation, this algorithm is superior to shortest path tree (SPT) technique and minimum delay maximum degree algorithm (MDMDA). This result is obtained according to certain simulation parameters and to the tool used to construct the graphs, regarding the total tree cost and the total tree flows criteria, when there is no delay constraint.

We present an alternate linear algorithm for finding the minimum flow in (s, t)-planar networks using a new concept of minimal removable sets developed here. The iterative nature of the algorithm facilitates the adjustment of solutions for systems in developmental stages. The minimum flow algorithm presented here requires O(|V|) time, where V denotes the set of vertices. The minimum flow problem arises in many transportation and communication systems.

This paper develops methods for the exact computation of the distribution of the maximum flow and related quantities in a planar network with independent and exponentially distributed arc capacities. A continuous time Markov chain (CTMC) with upper triangular rate matrix and single absorbing state is equal to the value of maximum flow in the network. Recursive algorithms are developed for computing the distribution and moments of the maximum flow. Algorithms are also presented to compute the probability that a given cut is the minimum capacity cut in the network. The algorithms are efficient and computationally stable. Distribution of the maximum flow, given a minimum cut, is studied. Keywords include: Maximum flow; Stochastic networks; Multi-state reliability modeling; Markov chains.