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A mathematical model of water pollution measurement in a stream using a collocation method with a higher order Legendre polynomial
(2025-08-01)
Thongtha, Kaboon
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Pochai, Nopparat
In environmental research, challenges with water contamination assessment are generally prevalent. Through data collection, pollution levels in a system may be determined. This is quite challenging and involved; the measurements of what was measured vary from one point to another in every location. The governing equations for a uniform flow pollution dispersion model are used in water quality modeling. The advection-diffusion-reaction equation used in water quality model-ing for a uniform flow stream is a stable pollution dispersion model. This study presents a one-dimensional mathematical model for measuring stream water quality by collocation higher order Legendre polynomial functions. A water pol-lutant concentration can be approximated using the collocation method. A related water quality quantification method may also be employed with the suggested mathematical simulation to approximate the solution.
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A simple mathematical model for assessing water quality in a closed-system shrimp farm
(2025-08-01)
Thongtha, Kaboon
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Pochai, Nopparat
The problem of wastewater from shrimp farming affects the environment, both in terms of wastewater discharge and soil deterioration. Wastewater management is also quite expensive for the production costs of shrimp farmers. Therefore, the approach to using shrimp farming technology in closed-system farms is proposed, which reduces wastewater discharge into the environment and reduces the cost of wastewater treatment for farmers. This research presents a simple mathematical model for assessing water quality in such closed-system shrimp farms. The method for determining various parameters for determining the mathematical model is presented. The model solution is estimated by the Runge-Kutta method of the fourth order. This research simulates the situation to compare the different parameter values in each situation, which affect the level of water quality in closed-system shrimp farms at different times. The research found that the initial water quality, the rate of chemical reaction of pollutants, the rate of pollution formation, the rate of pollution decomposition, the rate of decrease in pollution concentration due to water circulation between the farm and the water treatment pond, and time all affect water quality. The results from the calculation can help closed-system shrimp farmers know the trend of pollution concentration changes in closed-system shrimp farms in order to find ways to develop techniques for improving water quality.
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A Numerical Simulation of the Kratom Plant Growth Model While Treated by a Specific Nutrient Using an Explicit Finite Difference Method
(2025-01-01)
Krongsamsri, Pitchayapa
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Komthong, Nontalee
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Yammeng, Jidapa
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Chaichuay, Chinda
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Boonchom, Banjong
Kratom refers to both Mitragyna speciosa, a tree native to Southeast Asia, and products manufactured from its leaves sold as herbal supplements. Kratom leaves contain a range of chemical compounds known as bioactive alkaloids, which have physiological effects. A mathematical model of the Kratom plant under a particular nutritional treatment will be provided in this research. Also, the methods for setting the initial condition and boundary condition will be presented. Also, as the plant grows, the solution's domain shifts every time. Techniques for adjusting the specific nutrient's physical parameters are also provided. With the use of an explicit finite difference method, the solutions are approximated. The specific nutritional concentrations are calculated for each height level. As shown, the specific nutrient will spread from the root to the apex of the trunk. The nutrient has the capacity to stimulate the growth of the Kratom. The specific nutrient concentration along the trunk may be measured using the proposed mathematical model as the Kratom plant grows each day. A proposed numerical model with a specific nutrient can be used to develop a precise model, such as a one-dimensional model of branches and foliage. It would be more captivating if the plant nutrients indicated here were researched for their ability to accelerate the growth of large or medium-sized Kratom plants. In conclusion, the study shows that calcium dihydrogen phosphate monohydrate may be useful as a growth promoter for Kratom plants and suggests a way to measure its effects quantitatively.
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A Mathematical Model for Evaluating the Risk of Airborne Infection Among Bus Passengers Using Ventilation Systems
(2024-01-01)
Sooknum, Jenjira
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Pochai, Nopparat
Carbon dioxide from human breath contributes significantly to airborne diseases. Breathing can expose us to usually dangerous airborne infections, which rapidly spread. By using a bus, there is a chance of contracting an infection. This study takes into account a mathematical model of airborne infection caused by human breath. The purpose of this research is to evaluate the probability that passengers in a bus with ventilation systems may well get an airborne infection. The model can be divided into five submodels, such as an exhaled air concentration measurement model for a bus with a variable number of passengers, the volume fraction of exhaled air model, the concentration of airborne infectious particles model, the number of airborne infectious particles model, and the risk of airborne infection model. The model’s solution might be used to determine the probability that susceptible people will get an airborne infection. An explicit forward-time centered-space finite difference method is used to approximate the solution. In order to reduce the risk of airborne infection and improve ventilation, the provided mathematical models were used to assess the risk of airborne infection among bus passengers using ventilation systems. Better air quality control that balances the number of passengers allowed to travel on a bus will be among the ventilation’s main advantages.
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A Mathematical Model for the Evaluation of Airborne Infection Risk for Bus Passengers
(2023-03-01)
Sooknum, Jenjira
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Pochai, Nopparat
Human breath emits a lot of carbon dioxide, which contributes a lot to airborne infections. Airborne infections spread speedily, and breathing can expose us to life-threatening airborne infections. There is a risk of infection if people are traveling by bus. A mathematical model of carbon dioxide concentration measurement due to human breath is proposed in this research. The focus of this research is to determine the amount of carbon dioxide produced by bus passengers. The model's solution is approximated using an explicit finite difference technique. The model solution can be used to determine how much time passengers are willing to spend on the bus while carbon dioxide levels are kept under control. Furthermore, mathematical models were utilized to quantify the risk of air infection among bus passengers with ventilation systems, in order to reduce the risk of air infection and increase ventilation. The proposed air quality model was found to be in good agreement in that it allows us to know the balance between the number of passengers allowed to sit on the bus while managing the risk of airborne infection, carbon dioxide concentration, and ventilation system potential. A significant advantage of the ventilation will be better air quality control that balances the number of passengers permitted to ride on a bus
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A Non-Dimensional Mathematical Model of Shoreline Evolution with a Groin Structure Using an Unconditionally Stable Explicit Finite Difference Technique
(2022-01-01)
Manilam, Surasak
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Pochai, Nopparat
Abstract—Coastal erosion is a natural phenomenon that occurs when sediment transport away from the coast is not countered by the formation of new material on the shoreline. This is indeed a problem that is driving the erosion of coastal areas. A sea wall and a groin were created to prevent coastal erosion and floods. The future topography of the beach is being investigated using shoreline evolution analysis. Erosion, accretion, and sea level changes are basic stages that have a significant impact on the coastal structure. A qualitative analysis of the model coastal behavior in relation to the controlling process is required to research beach erosion and beach deposition. When stated in terms of non-dimensional variables, all are mathematically equivalent. In general, the models do not have to be dimensionally different. Those might just be modifications of the same problems. One can solve a wide range of models with a single solution to the related nondimensional equation. In this research, we provide a governing equation when a groin is introduced to a one-dimensional shoreline growth model. A non-dimensional shoreline evolution model with a groin structure model is provided. The model now has the ability to manipulate physical parameters. When groin structural effects are present, the initial condition setting method and boundary condition approaches are also given. To approximate the incremental model in each year, the forward time-centered space technique and the unconditionally stable Saulyev finite difference methods are used. The Saulyev finite difference approach can handle numerical solutions in almost any scenario since the stability requirements are not restricted. The Saulyev finite difference technique can be very useful for computing a practical conceptual design of shoreline evolution since the number of grids has increased. The numerical models offered provide a viable simulation for evaluating long-term coastal development. The proposed modeling may be used to forecast the effectiveness of constructing a groin system on a local beach.
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A Shoreline Evolution Model With the Wavelength Effect of Breaking Waves on Groin Structures
(2022-01-01)
Unyapoti, Pidok
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Pochai, Nopparat
Local sea level rise, strong wave action, and tidal currents all wear down or carry away rocks, soil, and sand along the beaches. The quantity of beach areas has decreased as a result of this issue. Analyzing the progression of the shoreline can help us better understand how the beach will look in the future. A groin structure was built to stop beach erosion and repair the beach. Beach erosion and beach deposition research requires a qualitative analysis of the model shoreline behavior in connection to the governing process. Models for shoreline evolution are the subject of some research. However, they focus on the shoreline evolution in an area between a couple of groin structures. The investigated area of shoreline evolution with a pair of groin structures is enlarged in this research to include the groin system and surrounding area. A more realistic shoreline evolution model has been presented, which takes into account the wavelength influence of breaking waves on groin constructions. The initial condition setting approach and boundary conditions techniques, as well as various groin structural impacts, are discussed. A wave crest impact model and five wavelength effects of breaking waves are introduced. Each year, the coastline evolution is approximated using the classical forward-time centered-space method and the unconditionally stable Saulyev finite differential methods. The estimated impacts of shoreline evolution were consistent with the wave crest impact model for five case wavelengths. For assessing long coastline evolution, the numerical models presented enable a reasonable simulation. The efficiency of building a groin system on a nearby beach might be predicted using the proposed modeling.
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A shoreline evolution model with a groin structure under non-uniform breaking wave crest impact
(2021-04-01)
Unyapoti, Pidok
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Pochai, Nopparat
Beach erosion is a natural phenomenon that is not compensated by depositing fresh material on the shoreline while transporting sand away from the shoreline. There are three phenomena that have a serious influence on the coastal structure, such as increases in flooding, accretion, and water levels. In addition, the prediction of coastal evolution is used to investigate the topography of the beach. In this research, we present a one-dimensional mathematical model of shoreline evolution, and the parameters that influence this model are described on a monthly basis over a period of one year. Consideration is given to the wave crest impact model for evaluating the impact of the wave crest at that stage. It focuses on the evolution of the shoreline in environments where groins are installed on both sides. The initial and boundary condition setting techniques are proposed by the groins and their environmental parameters. The non-uniform influence of the crest of the breaking wave is so often considered. We then used the traditional forward time centered space technique and the Saulyev finite difference technique to estimate the monthly evolution of the shoreline for each year.
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A shoreline evolution model with a twin groins structure using unconditionally stable explicit finite difference techniques
(2021-01-01)
Unyapoti, Pidok
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Pochai, Nopparat
Beach erosion is a natural process that occurs when conveying sediment away from the shoreline is not balanced by depositing new material on the shoreline. This is a problem that is causing beach areas to decline. To avoid beach erosion and flooding, a sea wall and groin have been built. Shoreline evolution prediction is used to investigate the beach topography in the future. There are three phenomena give a large effect to the coastal structure such as the erosion, the accretion and the water level changes. To investigate of beach erosion and beach deposition is needed qualitative understanding of idealized shoreline response to the governing process. In this research, we introduce a governing equation of a one-dimensional shoreline evolution model when a couple of groins is added. The introduced model is a transient one-line model. The manipulation of physical parameters for the model is introduced. The setting method of the initial condition and the boundary conditions techniques when a couple of groin structure effect are also proposed. The traditional forward time centered space method and the unconditionally stable Saulyev finite difference methods are employed to approximate the incremental model in each year. The proposed numerical models give practically simulation for long-term shoreline evolution investigation. The proposed simulation can be used to predict the efficiency of a groin system construction in a local beach. The model is a tool for environment impact assessment of a installing groin structure project.
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A numerical treatment of air flow model in the area under the station platform of Thailand BTS sky train
(2010-12-01)
Pochai, Nopparat
Problem statement: The area under Phayathai station platform of sky train in Bangkok, Thailand, has a problem of air pollution control. Approach:The Bangkok Mass Transit System Company tries to set up the electric fans inside the area for air flow improvement. Results: The flow of the air is still not smooth and the air quality is still lower than standard. The assumption of the research that is the flow obstructs by the platform structures. Conclusion: In this research, a mathematical model can be simulating the causes of the flow obstacle. The numerical solution of the model is obtained by using a finite element technique. © 2010 Science Publications.

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