A numerical solution of Richards equation: a simple method adaptable in parallel computing

“…For this, an explicit scheme is the best option. In [12], a linearized Richards equation model is studied. In [8], stability analysis of an explicit scheme for the Richards equation is studied.…”

Section: Introductionmentioning

confidence: 99%

An Explicit Stabilized Runge–Kutta–Legendre Super Time-Stepping Scheme for the Richards Equation

Timsina

Khanal

Uprety

2021

Mathematical Problems in Engineering

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“…The proof is based on the superposition principle, being the heat equation a linear partial differential equation. Thus, it is sufficient to add the solution of the associated homogeneous equation, i.e., with f = 0, satisfying the inhomogeneous initial condition and the solution of problem (11) equipped with initial condition g = 0, see [28] for the complete proof of this theorem.…”

Section: The Solution Of the Forced Heat Transfer Problemmentioning

confidence: 99%

“…The rainwater infiltrations [11] and aquifer movements can influence the heat propagation in the soil. However, the estimation of soil moisture dynamics is not an easy task, it requires complex geological surveys and the evaluation of rainwater effects in a long-term perspective.…”

Section: Introductionmentioning

confidence: 99%

Inverse heat conduction to model and optimise a geothermal field

Egidi¹,

Giacomini²,

Maponi³

2021

Preprint

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The design of heat exchanger fields is a key phase to ensure the long-term sustainability of such renewable energy systems. This task has to be accomplished by modelling the relevant processes in the complex system made up of different exchangers, where the heat transfer must be considered within exchangers and outside exchangers. We propose a mathematical model for the study of the heat conduction into the soil as consequence of the presence of exchangers. Such a problem is formulated and solved with an analytical approach. On the basis of such analytical solution, we propose an optimisation procedure to compute the best position of the exchangers by minimising the adverse effects of neighbouring devices. Some numerical experiments are used to show the effectiveness of the proposed method also by taking into account a reference approximation procedure of the problem based on a finite difference method.

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“…For this, an Forward Euler scheme is the best option. In [13], a linearized Richards equation model is studied. In [9], stability analysis of Forward Euler scheme for the Richards equation is studied.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Water Flow in Unsaturated Soil with Evapotraspiration

Timsina

Khanal

Ludu

et al. 2021

Nepali Math. Sci. Rep.

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Flow movement in unsaturated soil can be expressed by Richards equation. This equation can be obtained by applying the mass conversation law and the Darcy law. In this work, we solve one-dimensional Kirchhoff transformed Richards equation with loss of water due to the evaporation of unsaturated porous media (soils) and transpiration of plants numerically using Crank-Nicolson method. The result has compared with evapotranspiration function and without it in the governing equation. It has found that an additional work in time and flow movement is needs to reach the given boundary condition for the model without evapotranspiration.

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A numerical solution of Richards equation: a simple method adaptable in parallel computing

Cited by 12 publications

References 32 publications

An Explicit Stabilized Runge–Kutta–Legendre Super Time-Stepping Scheme for the Richards Equation

An Explicit Stabilized Runge–Kutta–Legendre Super Time-Stepping Scheme for the Richards Equation

Inverse heat conduction to model and optimise a geothermal field

Numerical Solution of Water Flow in Unsaturated Soil with Evapotraspiration

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