THE POLLUTANT TRANSPORT EQUATION FOR A STEADY, GRADUALLY VARIED FLOW IN AN OPEN CHANNEL NETWORK: A SOLUTION OF HIGH ACCURACY
The paper is concerned with solving the transport pollutant problem for a steady, gradually varied flow in an open channel network. The 1D advective-diffusive transport equation is solved using the splitting technique. An analytical solution of the linear advective diffusive equation in the form of...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Gdańsk University of Technology
2007-10-01
|
| Series: | TASK Quarterly |
| Subjects: | |
| Online Access: | https://journal.mostwiedzy.pl/TASKQuarterly/article/view/2059 |
| _version_ | 1818208088927240192 |
|---|---|
| author | ROMUALD SZYMKIEWICZ |
| author_facet | ROMUALD SZYMKIEWICZ |
| author_sort | ROMUALD SZYMKIEWICZ |
| collection | DOAJ |
| description |
The paper is concerned with solving the transport pollutant problem for a steady, gradually varied flow in an open channel network. The 1D advective-diffusive transport equation is solved using the splitting technique. An analytical solution of the linear advective diffusive equation in the form of an impulse response function is used to solve the advection-diffusion part of the governing equation. This approach, previously applied in solutions of the advection-diffusion equation for a single channel, is extended to a channel network. Numerical calculations are only required to compute the integral of convolution. The finite difference method is used to solve the second part of the governing equation, containing the source term. The applied approach has considerable advantages, especially appreciable in the case of advection-dominated transport with large gradients of concentration, since it generates no numerical dissipation or dispersion.
The flow parameters are obtained via solution of the steady, gradually varied flow equation. In the final non-linear system of algebraic equations obtained through approximation of the ordinary differential equation, the depths at each cross-section of channels and the discharge at each branch of the network are considered as unknowns. The system is solved using the modified Picard iteration, which ensures convergence of the iterative process for a steady, gradually varied flow solved for both looped and tree-type open channel networks.
|
| first_indexed | 2024-12-12T04:39:16Z |
| format | Article |
| id | doaj.art-0bf09cedcde1414ba37223feba227f9c |
| institution | Directory Open Access Journal |
| issn | 1428-6394 |
| language | English |
| last_indexed | 2024-12-12T04:39:16Z |
| publishDate | 2007-10-01 |
| publisher | Gdańsk University of Technology |
| record_format | Article |
| series | TASK Quarterly |
| spelling | doaj.art-0bf09cedcde1414ba37223feba227f9c2022-12-22T00:37:51ZengGdańsk University of TechnologyTASK Quarterly1428-63942007-10-01114THE POLLUTANT TRANSPORT EQUATION FOR A STEADY, GRADUALLY VARIED FLOW IN AN OPEN CHANNEL NETWORK: A SOLUTION OF HIGH ACCURACYROMUALD SZYMKIEWICZ0Gdansk University of Technology, Faculty of Civil and Environmental Engineering The paper is concerned with solving the transport pollutant problem for a steady, gradually varied flow in an open channel network. The 1D advective-diffusive transport equation is solved using the splitting technique. An analytical solution of the linear advective diffusive equation in the form of an impulse response function is used to solve the advection-diffusion part of the governing equation. This approach, previously applied in solutions of the advection-diffusion equation for a single channel, is extended to a channel network. Numerical calculations are only required to compute the integral of convolution. The finite difference method is used to solve the second part of the governing equation, containing the source term. The applied approach has considerable advantages, especially appreciable in the case of advection-dominated transport with large gradients of concentration, since it generates no numerical dissipation or dispersion. The flow parameters are obtained via solution of the steady, gradually varied flow equation. In the final non-linear system of algebraic equations obtained through approximation of the ordinary differential equation, the depths at each cross-section of channels and the discharge at each branch of the network are considered as unknowns. The system is solved using the modified Picard iteration, which ensures convergence of the iterative process for a steady, gradually varied flow solved for both looped and tree-type open channel networks. https://journal.mostwiedzy.pl/TASKQuarterly/article/view/2059steady gradually varied flowadvection-diffusion equationsplitting techniqueintegral of convolution |
| spellingShingle | ROMUALD SZYMKIEWICZ THE POLLUTANT TRANSPORT EQUATION FOR A STEADY, GRADUALLY VARIED FLOW IN AN OPEN CHANNEL NETWORK: A SOLUTION OF HIGH ACCURACY TASK Quarterly steady gradually varied flow advection-diffusion equation splitting technique integral of convolution |
| title | THE POLLUTANT TRANSPORT EQUATION FOR A STEADY, GRADUALLY VARIED FLOW IN AN OPEN CHANNEL NETWORK: A SOLUTION OF HIGH ACCURACY |
| title_full | THE POLLUTANT TRANSPORT EQUATION FOR A STEADY, GRADUALLY VARIED FLOW IN AN OPEN CHANNEL NETWORK: A SOLUTION OF HIGH ACCURACY |
| title_fullStr | THE POLLUTANT TRANSPORT EQUATION FOR A STEADY, GRADUALLY VARIED FLOW IN AN OPEN CHANNEL NETWORK: A SOLUTION OF HIGH ACCURACY |
| title_full_unstemmed | THE POLLUTANT TRANSPORT EQUATION FOR A STEADY, GRADUALLY VARIED FLOW IN AN OPEN CHANNEL NETWORK: A SOLUTION OF HIGH ACCURACY |
| title_short | THE POLLUTANT TRANSPORT EQUATION FOR A STEADY, GRADUALLY VARIED FLOW IN AN OPEN CHANNEL NETWORK: A SOLUTION OF HIGH ACCURACY |
| title_sort | pollutant transport equation for a steady gradually varied flow in an open channel network a solution of high accuracy |
| topic | steady gradually varied flow advection-diffusion equation splitting technique integral of convolution |
| url | https://journal.mostwiedzy.pl/TASKQuarterly/article/view/2059 |
| work_keys_str_mv | AT romualdszymkiewicz thepollutanttransportequationforasteadygraduallyvariedflowinanopenchannelnetworkasolutionofhighaccuracy AT romualdszymkiewicz pollutanttransportequationforasteadygraduallyvariedflowinanopenchannelnetworkasolutionofhighaccuracy |