A cell-vertex finite volume scheme for solute transport equations in open channel networks

Yoshioka, Hidekazu; Unami, Koichi

doi:10.1016/j.probengmech.2012.12.001

Cited by 25 publications

(32 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The FVM, which is referred to as the Dual-Finite Volume Method (DFVM) [1,13], is used for numerically solving (3). Detailed discretization of the DFVM for linear advection-diffusion equations is described in Yoshioka and Unami [1].…”

Section: Finite Volume Methodsmentioning

confidence: 99%

“…Detailed discretization of the DFVM for linear advection-diffusion equations is described in Yoshioka and Unami [1]. The DFVM here follows that of Yoshioka and Unami [1] except for treatment of nonlinearity and degeneration of the coefficients. The domain is discretized into nodes and regular cells (elements) as in the conventional FVMs, so that one vertex falls exactly on one node.…”

Section: Finite Volume Methodsmentioning

confidence: 99%

“…The domain is discretized into nodes and regular cells (elements) as in the conventional FVMs, so that one vertex falls exactly on one node. A vertex associates a dual cell, which is a 1-D analogue of the Voronoi cell [1]. The solution u and the flux F are distributed on the dual and regular cells, respectively, considering that a ball B(y, r) in (3) corresponds to a dual cell.…”

Section: Finite Volume Methodsmentioning

confidence: 99%

“…1); however, no or at most only a few researches numerically solved nonlinear and degenerate diffusion equations in connected graphs, which is a major motivation of our research. This paper shows that an FVM [1,13] achieves the above-mentioned objective, which can handle a variety of realistic conditions on the model parameters and initial and boundary conditions. Unresolved issues on the mathematical model and the numerical method to be addressed in a future are finally discussed.…”

Section: Introductionmentioning

confidence: 91%

“…Diffusion-type partial differential equations (PDEs) on connected graphs arise as relevant mathematical models for transport phenomena in environmental [1,2], biological [3], and material problems [4,5]. Here a connected graph is defined as an union of 0-D vertices that links 1-D intervals [6].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Numerical modelling of nonlinear and degenerate diffusion equations on connected graphs: application to moisture dynamics in non-woven fibrous strip networks

2016

Self Cite

View full text Add to dashboard Cite

A numerical model of a nonlinear and degenerate diffusion equation on connected graphs, arising in a diversity of industrial applications, is presented. This paper shows that concurrently using a staggered finite volume spatial discretization with an analytical solution-based flux evaluation method and an operator-splitting technique computes stable and physicallyconsistent numerical solutions to the equation. A demonstrative application example of the numerical model to moisture dynamics in a hypothetical non-woven fibrous strip network under an evaporative environment is presented in order to show its versatility. Mathematical issues to be addressed in a future for better comprehending the model are finally discussed.

show abstract

Section: Finite Volume Methodsmentioning

confidence: 99%

Section: Finite Volume Methodsmentioning

confidence: 99%

Section: Finite Volume Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical modelling of nonlinear and degenerate diffusion equations on connected graphs: application to moisture dynamics in non-woven fibrous strip networks

2016

Self Cite

View full text Add to dashboard Cite

show abstract

Optimization model to start harvesting in stochastic aquaculture system

Yoshioka

Yaegashi

2017

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

Establishment of cost-effective management strategy of aquaculture is one of the most important issues in fishery science, which can be addressed with bio-economic mathematical modeling. This paper deals with the aforementioned issue using a stochastic process model for aquacultured non-renewable fishery resources from the viewpoint of an optimal stopping (timing) problem. The goal of operating the model is to find the optimal criteria to start harvesting the resources under stochastic environment, which turns out to be determined from the Bellman equation (BE). The BE has a separation of variables type structure and can be simplified to a reduced BE with a fewer degrees of freedom. Dependence of solutions to the original and reduced BEs on parameters and independent variables is analyzed from both analytical and numerical standpoints. Implications of the analysis results to management of aquaculture systems are presented as well. Numerical simulation focusing on aquacultured Plecoglossus altivelis in Japan validates the mathematical analysis results. Bus. Ind. 2017, 33 476-493 The quantity W * is related to Ψ that solves the reduced BE (12), and therefore, Ψ and W * have to be simultaneously solved. The curve C is therefore a free boundary. Assuming the unique existence of such C, the one-dimensional domain 0 < w < +∞ for each t < T can be separated into the two regions: the waiting region S 1 (t) = {w; Ψ (t, w) > w} and the Appl. Stochastic Models Bus. Ind. 2017, 33 476-493 Appl. Stochastic ModelsProof of Proposition 3.3 J ,t with p = ( p) i (i = 1, 2) is denoted as J ,t,i . For each ∈ t,T , the inequalitydirectly follows from (5). This leads to

show abstract

Robust stochastic control modeling of dam discharge to suppress overgrowth of downstream harmful algae

Yoshioka

Yaegashi

2017

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

The mathematical concept of multiplier robust control is applied to a dam operation problem, which is an urgent issue on river water environment, as a new industrial application of stochastic optimal control. The goal of the problem is to find a fit-for-purpose and environmentally sound operation policy of the flow discharge from a dam so that overgrowth of the harmful algae Cladophora glomerata Kützing in its downstream river is effectively suppressed. A minimal stochastic differential equation for the algae growth dynamics with uncertain growth rate is first presented. The performance index to be maximized by the operator of the dam while minimized by nature is formulated within the framework of differential games. The dynamic programming principle leads to a Hamilton-Jacobi-Bellman-Isaacs equation whose solution determines the worst-case optimal operation policy of the dam, ie, the policy that the operator wants to find. Application of the model to overgrowth suppression of Cladophora glomerata Kützing just downstream of a dam in a Japanese river is then carried out. Values of the model parameters are identified with which the model successfully reproduces the observed population dynamics. A series of numerical experiments are performed to find the most effective operation policy of the dam based on a relaxation of the current policy.

show abstract

A cell-vertex finite volume scheme for solute transport equations in open channel networks

Cited by 25 publications

References 35 publications

Numerical modelling of nonlinear and degenerate diffusion equations on connected graphs: application to moisture dynamics in non-woven fibrous strip networks

Numerical modelling of nonlinear and degenerate diffusion equations on connected graphs: application to moisture dynamics in non-woven fibrous strip networks

Optimization model to start harvesting in stochastic aquaculture system

Robust stochastic control modeling of dam discharge to suppress overgrowth of downstream harmful algae

Contact Info

Product

Resources

About