On the Shooting Method Applied to Richards’ Equation with a Forcing Term

A new high-performance numerical model (Frehg) is developed to simulate water flow in shallow coastal wetlands. Frehg solves the 2D depth-integrated, hydrostatic, Navier–Stokes equations (i.e., shallow-water equations) in the surface domain and the 3D variably-saturated Richards equation in the subsurface domain. The two domains are asynchronously coupled to model surface-subsurface exchange. The Frehg model is applied to evaluate model sensitivity to a variety of simplifications that are commonly adopted for shallow wetland models, especially the use of the diffusive wave approximation in place of the traditional Saint-Venant equations for surface flow. The results suggest that a dynamic model for momentum is preferred over diffusive wave model for shallow coastal wetlands and marshes because the latter fails to capture flow unsteadiness. Under the combined effects of evaporation and wetting/drying, using diffusive wave model leads to discrepancies in modeled surface-subsurface exchange flux in the intertidal zone where strong exchange processes occur. It indicates shallow wetland models should be built with (i) dynamic surface flow equations that capture the timing of inundation, (ii) complex topographic features that render accurate spatial extent of inundation, and (iii) variably-saturated subsurface flow solver that is capable of modeling moisture change in the subsurface due to evaporation and infiltration.

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Modelling Tree Growth in Monospecific Forests from Forest Inventory Data

Forests ◽

10.3390/f12060753 ◽

2021 ◽

Vol 12 (6) ◽

pp. 753

Author(s):

Guadalupe Sáez-Cano ◽

Marcos Marvá ◽

Paloma Ruiz-Benito ◽

Miguel A. Zavala

Keyword(s):

Tree Growth ◽

Large Scale ◽

Temporal Dynamics ◽

Carbon Sink ◽

Size Variation ◽

Biotic Interactions ◽

Richards Equation ◽

Tree Level ◽

Forest Inventories ◽

Large Scale Data

The prediction of tree growth is key to further understand the carbon sink role of forests and the short-term forest capacity on climate change mitigation. In this work, we used large-scale data available from three consecutive forest inventories in a Euro-Mediterranean region and the Bertalanffy–Chapman–Richards equation to model up to a decade’s tree size variation in monospecific forests in the growing stages. We showed that a tree-level fitting with ordinary differential equations can be used to forecast tree diameter growth across time and space as function of environmental characteristics and initial size. This modelling approximation was applied at different aggregation levels to monospecific regions with forest inventories to predict trends in aboveground tree biomass stocks. Furthermore, we showed that this model accurately forecasts tree growth temporal dynamics as a function of size and environmental conditions. Further research to provide longer term prediction forest stock dynamics in a wide variety of forests should model regeneration and mortality processes and biotic interactions.

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Mathematical analysis of bio-convective micropolar nanofluid

Journal of Computational Design and Engineering ◽

10.1016/j.jcde.2019.04.001 ◽

2019 ◽

Vol 6 (3) ◽

pp. 233-242 ◽

Cited By ~ 10

Author(s):

Sohail Nadeem ◽

Muhammad Naveed Khan ◽

Noor Muhammad ◽

Shafiq Ahmad

Keyword(s):

Differential Equations ◽

Microbial Fuel Cells ◽

Shooting Method ◽

Stretching Sheet ◽

Volume Fraction ◽

Three Dimensional ◽

Convection Flow ◽

Micropolar Nanofluid ◽

Exponentially Stretching ◽

Micro Organisms

Abstract The present investigation concentrates on three dimensional unsteady forced bio-convection flow of a viscous fluid. An incompressible flow of a micropolar nanofluid encloses micro-organisms past an exponentially stretching sheet with magnetic field is analyzed. By employing convenient transformation the partial differential equations are converted into the ordinary differential equations which are non-linear. By using shooting method to solved these equations numerically. The influence of the determining parameters on the velocity, temperature, micro-rotation, nanoparticle volume fraction, microorganism are incorporated. The skin friction, heat transfer rate, and the microorganism rate are analyzed. The results depicts that the value of the wall shear stress and Nusselt number are declined while an enhancement take place in the microorganism number. The slip parameters increases the velocity, thermal energy, and microorganism number consequentially. The present investigation are important in improving achievement of microbial fuel cells.

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