Spatio-Temporal Modeling and Simulation of Asian Soybean Rust Based on Fuzzy System

Mato Grosso, Brazil, is the largest soy producer in the country. Asian Soy Rust is a disease that has already caused a lot of damage to Brazilian agribusiness. The plant matures prematurely, hindering the filling of the pod, drastically reducing productivity. It is caused by the Phakopsora pachyrhizi fungus. For a plant disease to establish itself, the presence of a pathogen, a susceptible plant, and favorable environmental conditions are necessary. This research developed a fuzzy system gathering these three variables as inputs, having as an output the vulnerability of the region to the disease. The presence of the pathogen was measured using a diffusion-advection equation appropriate to the problem. Some coefficients were based on the literature, others were measured by a fuzzy system and others were obtained by real data. From the mapping of producing properties, the locations where there are susceptible plants were established. And the favorable environmental conditions were also obtained from a fuzzy system, whose inputs were temperature and leaf wetness. Data provided by IBGE, INMET, and Antirust Consortium were used to fuel the model, and all treatments, tests, and simulations were carried out within the Matlab® environment. Although Asian Soybean Rust was the chosen disease here, the model was general in nature, so could be reproduced for any disease of plants with the same profile.

Intuitionistic fuzzy transport equation

In the present paper, we use the generalized differentiability concept to study the intuitionistic fuzzy transport equation. We consider transport equation in the homogeneous and non-homogeneous cases with intuitionistic fuzzy initial condition. To illustrate the results, we will solve an advection equation using the finite difference method.

Adaptive method for the solution of 1D and 2D advection–diffusion equations used in environmental engineering

The paper concerns the numerical solution of one-dimensional (1D) and two-dimensional (2D) advection–diffusion equations. For the numerical solution of the 1D advection–diffusion equation, a method, originally proposed for the solution of the 1D pure advection equation, has been developed. A modified equation analysis carried out for the proposed method allowed increasing of the resulting solution accuracy and, consequently, to reduce the numerical dissipation and dispersion. This is achieved by proper choice of the involved weighting parameter being a function of the Courant number and the diffusive number. The method is adaptive because for uniform grid point and for uniform flow velocity, the weighting parameter takes a constant value, whereas for non-uniform grid and for varying flow velocity, its value varies in the region of solution. For the solution of the 2D transport equation, the dimensional decomposition in the form of Strang splitting technique is used. Consequently, this equation is reduced to a series of the 1D equations with regard to x- and y-directions which next are solved using the aforementioned method. The results of computational experiments compared with the exact solutions confirmed that the proposed approaches ensure high solution accuracy of the transport equations.

Inverses of SBP-SAT Finite Difference Operators Approximating the First and Second Derivative

The scalar, one-dimensional advection equation and heat equation are considered. These equations are discretized in space, using a finite difference method satisfying summation-by-parts (SBP) properties. To impose the boundary conditions, we use a penalty method called simultaneous approximation term (SAT). Together, this gives rise to two semi-discrete schemes where the discretization matrices approximate the first and the second derivative operators, respectively. The discretization matrices depend on free parameters from the SAT treatment. We derive the inverses of the discretization matrices, interpreting them as discrete Green’s functions. In this direct way, we also find out precisely which choices of SAT parameters that make the discretization matrices singular. In the second derivative case, it is shown that if the penalty parameters are chosen such that the semi-discrete scheme is dual consistent, the discretization matrix can become singular even when the scheme is energy stable. The inverse formulas hold for SBP-SAT operators of arbitrary order of accuracy. For second and fourth order accurate operators, the inverses are provided explicitly.

AENO: a Novel Reconstruction Method in Conjunction with ADER Schemes for Hyperbolic Equations

In this paper, we present a novel spatial reconstruction scheme, called AENO, that results from a special averaging of the ENO polynomial and its closest neighbour, while retaining the stencil direction decided by the ENO choice. A variant of the scheme, called m-AENO, results from averaging the modified ENO (m-ENO) polynomial and its closest neighbour. The concept is thoroughly assessed for the one-dimensional linear advection equation and for a one-dimensional non-linear hyperbolic system, in conjunction with the fully discrete, high-order ADER approach implemented up to fifth order of accuracy in both space and time. The results, as compared to the conventional ENO, m-ENO and WENO schemes, are very encouraging. Surprisingly, our results show that the $$L_{1}$$ L 1 -errors of the novel AENO approach are the smallest for most cases considered. Crucially, for a chosen error size, AENO turns out to be the most efficient method of all five methods tested.

A Monotonic Method of Split Particles

The problem of correct calculation of the motion of a multicomponent (multimaterial) medium is the most serious problem for Lagrangian–Eulerian and Eulerian techniques, especially in multicomponent cells in the vicinity of interfaces. There are two main approaches to solving the advection equation for a multicomponent medium. The first approach is based on the identification of interfaces and determining their position at each time step by the concentration field. In this case, the interface can be explicitly distinguished or reconstructed by the concentration field. The latter algorithm is the basis of widely used methods such as VOF. The second approach involves the use of the particle or marker method. In this case, the material fluxes of substances are determined by the particles with which certain masses of substances bind. Both approaches have their own advantages and drawbacks. The advantages of the particle method consist in the Lagrangian representation of particles and the possibility of” drawbacks. The main disadvantage of the particle method is the strong non-monotonicity of the solution caused by the discrete transfer of mass and mass-related quantities from cell to cell. This paper describes a particle method that is free of this drawback. Monotonization of the particle method is performed by spliting the particles so that the volume of matter flowing out of the cell corresponds to the volume calculated according to standard schemes of Lagrangian–Eulerian and Eulerian methods. In order not to generate an infinite chain of spliting, further split particles are re-united when certain conditions are met. The method is developed for modeling 2D and 3D gas-dynamic flows with accompanying processes, in which it is necessary to preserve the history of the process at Lagrangian points.