Analytical solution for Richards’ Equation ABSTRACT : Richards’ equation is a non-linear partial ... more Analytical solution for Richards’ Equation ABSTRACT : Richards’ equation is a non-linear partial differential equation that governs the process of infiltration and flow in non-saturated soils. A new analytical solution was developed for a one-dimensional vertical infiltration in homogeneous soils. The lower boundary condition is a constant pressure head and the upper boundary is given by a transient infiltration function in the form qB + (qC - qB)(e- at - e- bt). Exponential functional forms K = KSe αψ and θ = θ r + ( θ S - θ r)e αψ are used to represent the hydraulic conductivity and pressure relation and the soil water retention curve, respectively. Steady state profiles are used as initial condition. Hydraulic behaviors of homogeneous soils are discussed in terms of pressure head profiles for different infiltration curves and soil parameters. Key-words: Richards’ equation; analytical solution.
Environmental issues associated with greenhouse gases emission, notably methane, carbon dioxide a... more Environmental issues associated with greenhouse gases emission, notably methane, carbon dioxide and nitrous oxide in reservoirs became a source of interest due to studies published in the 90s, which highlighted the potential negative impact of this energy source. Studies which followed these premises have focused on measuring the fluxes of these gases without, however, qualifying mathematical models for an accurate estimate of these fluxes. In this context, this paper presents a zero-dimensional mathematical model capable of estimating the diffusive and bubbling fluxes of carbon dioxide (CO2) and methane (CH4). The model incorporates the dynamics of organic and inorganic carbon in dissolved and particulate fractions, their interactions with the sediment together with the influence of meteorological and hydrological forcings. The model was calibrated based on data measured in Capivari Reservoir (Paraná) and applied for a period of 43 years. The results are promising because of its co...
Analytical solution for Richards’ Equation
ABSTRACT : Richards’ equation is a non-linear parti... more Analytical solution for Richards’ Equation
ABSTRACT : Richards’ equation is a non-linear partial differential equation that governs the process of infiltration and flow in non-saturated soils. A new analytical solution was developed for a one-dimensional vertical infiltration in homogeneous soils. The lower boundary condition is a constant pressure head and the upper boundary is given by a transient infiltration function in the form qB + (qC - qB)(e- at - e- bt). Exponential functional forms K = KSe αψ and θ = θ r + ( θ S - θ r)e αψ are used to represent the hydraulic conductivity and pressure relation and the soil water retention curve, respectively. Steady state profiles are used as initial condition. Hydraulic behaviors of homogeneous soils are discussed in terms of pressure head profiles for different infiltration curves and soil parameters. Key-words: Richards’ equation; analytical solution.
Numerical Errors of the Richards Equation Using the Finite Volumes Method
ABSTRACT :The Richard... more Numerical Errors of the Richards Equation Using the Finite Volumes Method
ABSTRACT :The Richards equation is a non-linear partial differential equation that governs the process of infiltration and flow in unsaturated soils. An analytical solution is used to evaluate the accuracy and performance of the equation solution using the finite volumes method. The lower boundary condition is a prescribed pressure head and the upper boundary condition is a constant flow rate. Nine cases were simulated by varying the mesh refinement in time and space. The temporal evolution of the errors behaves similarly to an advective-diffusive process, propagating the error in the direction of flow and attenuating it as time advances. Errors and mass conservation are independent of the space grid and are much improved when reducing the time step. The behavior of secondary variables error is the same. Key-words: Finite volumes; Richards equation; analytic solution; numerical errors.
Analytical solution for Richards’ Equation ABSTRACT : Richards’ equation is a non-linear partial ... more Analytical solution for Richards’ Equation ABSTRACT : Richards’ equation is a non-linear partial differential equation that governs the process of infiltration and flow in non-saturated soils. A new analytical solution was developed for a one-dimensional vertical infiltration in homogeneous soils. The lower boundary condition is a constant pressure head and the upper boundary is given by a transient infiltration function in the form qB + (qC - qB)(e- at - e- bt). Exponential functional forms K = KSe αψ and θ = θ r + ( θ S - θ r)e αψ are used to represent the hydraulic conductivity and pressure relation and the soil water retention curve, respectively. Steady state profiles are used as initial condition. Hydraulic behaviors of homogeneous soils are discussed in terms of pressure head profiles for different infiltration curves and soil parameters. Key-words: Richards’ equation; analytical solution.
Environmental issues associated with greenhouse gases emission, notably methane, carbon dioxide a... more Environmental issues associated with greenhouse gases emission, notably methane, carbon dioxide and nitrous oxide in reservoirs became a source of interest due to studies published in the 90s, which highlighted the potential negative impact of this energy source. Studies which followed these premises have focused on measuring the fluxes of these gases without, however, qualifying mathematical models for an accurate estimate of these fluxes. In this context, this paper presents a zero-dimensional mathematical model capable of estimating the diffusive and bubbling fluxes of carbon dioxide (CO2) and methane (CH4). The model incorporates the dynamics of organic and inorganic carbon in dissolved and particulate fractions, their interactions with the sediment together with the influence of meteorological and hydrological forcings. The model was calibrated based on data measured in Capivari Reservoir (Paraná) and applied for a period of 43 years. The results are promising because of its co...
Analytical solution for Richards’ Equation
ABSTRACT : Richards’ equation is a non-linear parti... more Analytical solution for Richards’ Equation
ABSTRACT : Richards’ equation is a non-linear partial differential equation that governs the process of infiltration and flow in non-saturated soils. A new analytical solution was developed for a one-dimensional vertical infiltration in homogeneous soils. The lower boundary condition is a constant pressure head and the upper boundary is given by a transient infiltration function in the form qB + (qC - qB)(e- at - e- bt). Exponential functional forms K = KSe αψ and θ = θ r + ( θ S - θ r)e αψ are used to represent the hydraulic conductivity and pressure relation and the soil water retention curve, respectively. Steady state profiles are used as initial condition. Hydraulic behaviors of homogeneous soils are discussed in terms of pressure head profiles for different infiltration curves and soil parameters. Key-words: Richards’ equation; analytical solution.
Numerical Errors of the Richards Equation Using the Finite Volumes Method
ABSTRACT :The Richard... more Numerical Errors of the Richards Equation Using the Finite Volumes Method
ABSTRACT :The Richards equation is a non-linear partial differential equation that governs the process of infiltration and flow in unsaturated soils. An analytical solution is used to evaluate the accuracy and performance of the equation solution using the finite volumes method. The lower boundary condition is a prescribed pressure head and the upper boundary condition is a constant flow rate. Nine cases were simulated by varying the mesh refinement in time and space. The temporal evolution of the errors behaves similarly to an advective-diffusive process, propagating the error in the direction of flow and attenuating it as time advances. Errors and mass conservation are independent of the space grid and are much improved when reducing the time step. The behavior of secondary variables error is the same. Key-words: Finite volumes; Richards equation; analytic solution; numerical errors.
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Papers by Michael Mannich
ABSTRACT : Richards’ equation is a non-linear partial differential equation that governs the process of infiltration and flow in non-saturated soils. A new analytical solution was developed for a one-dimensional vertical infiltration in homogeneous soils. The lower boundary condition is a constant pressure head and the upper boundary is given by a transient infiltration function in the form qB + (qC - qB)(e- at - e- bt). Exponential functional forms K = KSe αψ and θ = θ r + ( θ S - θ r)e αψ are used to represent the hydraulic conductivity and pressure relation and the soil water retention curve, respectively. Steady state profiles are used as initial condition. Hydraulic behaviors of homogeneous soils are discussed in terms of pressure head profiles for different infiltration curves and soil parameters.
Key-words: Richards’ equation; analytical solution.
ABSTRACT :The Richards equation is a non-linear partial differential equation that governs the process of infiltration and flow in unsaturated soils. An analytical solution is used to evaluate the accuracy and performance of the equation solution using the finite volumes method. The lower boundary condition is a prescribed pressure head and the upper boundary condition is a constant flow rate. Nine cases were simulated by varying the mesh refinement in time and space. The temporal evolution of the errors behaves similarly to an advective-diffusive process, propagating the error in the direction of flow and attenuating it as time advances. Errors and mass conservation are independent of the space grid and are much improved when reducing the time step. The behavior of secondary variables error is the same.
Key-words: Finite volumes; Richards equation; analytic solution; numerical errors.
ABSTRACT : Richards’ equation is a non-linear partial differential equation that governs the process of infiltration and flow in non-saturated soils. A new analytical solution was developed for a one-dimensional vertical infiltration in homogeneous soils. The lower boundary condition is a constant pressure head and the upper boundary is given by a transient infiltration function in the form qB + (qC - qB)(e- at - e- bt). Exponential functional forms K = KSe αψ and θ = θ r + ( θ S - θ r)e αψ are used to represent the hydraulic conductivity and pressure relation and the soil water retention curve, respectively. Steady state profiles are used as initial condition. Hydraulic behaviors of homogeneous soils are discussed in terms of pressure head profiles for different infiltration curves and soil parameters.
Key-words: Richards’ equation; analytical solution.
ABSTRACT :The Richards equation is a non-linear partial differential equation that governs the process of infiltration and flow in unsaturated soils. An analytical solution is used to evaluate the accuracy and performance of the equation solution using the finite volumes method. The lower boundary condition is a prescribed pressure head and the upper boundary condition is a constant flow rate. Nine cases were simulated by varying the mesh refinement in time and space. The temporal evolution of the errors behaves similarly to an advective-diffusive process, propagating the error in the direction of flow and attenuating it as time advances. Errors and mass conservation are independent of the space grid and are much improved when reducing the time step. The behavior of secondary variables error is the same.
Key-words: Finite volumes; Richards equation; analytic solution; numerical errors.