In the present paper, we develop an efficient and accurate numerical approach based on one-dimens... more In the present paper, we develop an efficient and accurate numerical approach based on one-dimensional-moving integrated radial basis function (1D-MIRBF) and fully implicit modified Picard method for simulating fluid movement in heterogeneous soils governed by the highly non-linear Richards equation. The major advantages of the proposed 1D-MIRBF method include (i) a banded sparse system matrix that helps reduce the computational cost; (ii) the Kronecker Delta property of the constructed shape functions, which helps impose the essential boundary conditions in an exact manner; and (iii) high accuracy and fast convergence rate owing to the use of the IRBF approximation. The performance of the present method is demonstrated through several 1--D and 2--D soil infiltration problems. Numerical results obtained are in agreement with other published results in the literature. This solver for moisture motion in soils will be incorporated into a surface-water-flow solver to handle the surface ...
We analyse a nonlinear partial differential equation modelling reaction-diffusion systems with no... more We analyse a nonlinear partial differential equation modelling reaction-diffusion systems with nonlocal coupling and reaction fronts of gasless combustion. The equation is of active-dissipative type, nonlinear, with 6th-order spatial derivative. To numerically solve the equations we use the one-dimensional integrated radial basis function network (1D-IRBFN)method. The method has been previously developed and successfully applied to several problems such as structural analysis, viscous and viscoelastic flows and fluid-structure interaction. A commonly used approach is to differentiate a function of interest to obtain approximate derivatives. However, this leads to a reduction in convergence rate for derivatives and this reduction is an increasing function of derivative order. Accordingly, differentiation magnifies errors. To avoid this problem and recognising that integration is a smoothing process, the proposed 1D-IRBFN method uses the integral formulation, where spectral approximan...
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020
In this paper, we investigate a wide range of dynamical regimes produced by the nonlinearly excit... more In this paper, we investigate a wide range of dynamical regimes produced by the nonlinearly excited phase (NEP) equation (a single sixth-order nonlinear partial differential equation) using a more advanced numerical method, namely, the integrated radial basis function network method. Previously, we obtained single-step spinning solutions of the equation using the Galerkin method. First, we verify the numerical solver through an exact solution of a forced version of the equation. Doing so, we compare the numerical results obtained for different space and time steps with the exact solution. Then, we apply the method to solve the NEP equation and reproduce the previously obtained spinning regimes. In the new series of numerical experiments, we find regimes in the form of spinning trains of steps/kinks comprising one, two, or three kinks. The evolution of the distance between the kinks is analyzed. Two different kinds of boundary conditions are considered: homogeneous and periodic. The ...
IOP Conference Series: Materials Science and Engineering, 2010
Page 1. Integrated-RBF network method for free vibration analysis of laminated composite plates T... more Page 1. Integrated-RBF network method for free vibration analysis of laminated composite plates This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2010 IOP Conf. Ser.: Mater. Sci. Eng. 10 012236 ...
International Journal for Numerical Methods in Fluids, 2012
SUMMARYThis paper presents a local moving least square‐one‐dimensional integrated radial basis fu... more SUMMARYThis paper presents a local moving least square‐one‐dimensional integrated radial basis function networks method for solving incompressible viscous flow problems using stream function‐vorticity formulation. In this method, the partition of unity method is employed as a framework to incorporate the moving least square and one‐dimensional integrated radial basis function networks techniques. The major advantages of the proposed method include the following: (i) a banded sparse system matrix which helps reduce the computational cost; (ii) the Kronecker‐ δ property of the constructed shape function which helps impose the essential boundary condition in an exact manner; and (iii) high accuracy and fast convergence rate owing to the use of integration instead of conventional differentiation to construct the local radial basis function approximations. Several examples including two‐dimensional (2D) Poisson problems, lid‐driven cavity flow and flow past a circular cylinder are consid...
Engineering Analysis With Boundary Elements, Oct 1, 2015
We propose a novel numerical approach based on incompressible smoothed particle hydrodynamics and... more We propose a novel numerical approach based on incompressible smoothed particle hydrodynamics and moving integrated radial basis function networks method, namely ISPH-MIRBFN, for solving incompressible viscous flow problems. In the ISPH method, the pressure is acquired from solving Poisson equation. In the present approach, the pressure Poisson equation is solved on a set of MIRBFN nodal points and the obtained results are then transferred to the SPH particles. The performance of the present method is investigated through several numerical examples including spin-down vortex, flows in a lid-driven closed-cavity and a lid-driven open-cavity with a prescribed bottom wall motion. Numerical results show that the proposed method reduces the spurious pressure fluctuations, yields a smoother pressure-field solution and maintains the computational efficiency when compared to the ISPH.
2021 ASABE Annual International Virtual Meeting, July 12-16, 2021
Abstract. This paper reports on the validation of two numerical approaches that were developed to... more Abstract. This paper reports on the validation of two numerical approaches that were developed to determine the effect of compaction on the soil water retention curve (WRC). The proposed approaches satisfactorily expanded the applicability of the van Genuchten (1980) model. In Approach 1, an optimization problem was solved to enable the van Genuchten model parameters α and η to be estimated for a range of soil bulk densities, based on the WRC of the corresponding non-compacted soil and the estimated saturation, residual, and permanent wilting-point (-1500 kPa) water contents of the compacted soil. In Approach 2, the parameter η was assumed to be unaffected by changes in soil bulk density. Subsequently, the parameter α was determined using an equation especially developed by this study. Compared with measured data, Approach 2 yielded slightly better predictions of the WRC than Approach 1. However, both numerical approaches may be used with confidence in a wider range of scenarios than those presented in this study. Across all soils, our analyses showed that relatively small increments in soil bulk density, due to compaction, can result in significant reductions in the available water storage capacity (AWSC) of soils; the effect being dependent on soil type and the relative increase in soil bulk density. Mechanization systems that mitigate, or where possible avoid, soil damage due to compaction (coupled with management practices that reduce loss of soil organic carbon) are encouraged. Quantification of the benefits of compaction avoidance, in terms of improved infiltration, soil water retention and water-use efficiency, as well as better predictions of the hydrology of compacted soils, may be possible through the application of the models reported in this study.
Abstract The machine acceleration introduced by H. J. Schulze has been a cornerstone of the bubbl... more Abstract The machine acceleration introduced by H. J. Schulze has been a cornerstone of the bubble-particle (BP) detachment theory. It connects the mean dissipation rate of turbulence energy of water in a flotation machine with the BP detachment. In a recent paper, we scrutinized the theory and recommended its extension to cover both the longitudinal (centrifugation) and transverse (shear) effects of water turbulence. Since there is a significant difference in the densities of water, solid particles, and air bubbles, it is unknown if the available determination of the machine acceleration using the “water particles” is a good approximation for the bubble-particle aggregates. This paper aims to provide an answer to this fundamental question. For simplicity, this paper focuses on the acceleration of solid particles in water. Specifically, we use the Basset-Boussinesq-Oseen equation to quantify the particle acceleration. The correlation method in combination with the isotropic turbulence theory is applied to predict the particle acceleration components for the full range of turbulence length scale. Comparing with Schulze’s model, our recent model shows that the particle inertia should be considered in calculating the machine acceleration, especially for large and/or heavy particles and high energy dissipation rate. Our numerical results show that the machine acceleration decreases with increasing particle size and density and increases with increasing dissipation rate of turbulent kinetic energy and turbulence intensity.
Abstract A new control volume approach is developed based on compact integrated radial basis func... more Abstract A new control volume approach is developed based on compact integrated radial basis function (CIRBF) stencils for solution of the highly nonlinear Richards equation describing transient water flow in variably saturated soils. Unlike the conventional control volume method, which is regarded as second-order accurate, the proposed approach has high-order accuracy owing to the use of a compact integrated radial basis function approximation that enables improved flux predictions. The method is used to solve the Richards equation for transient flow in 1D homogeneous and heterogeneous soil profiles. Numerical results for different boundary conditions, initial conditions and soil types are shown to be in good agreement with Warrick’s semi-analytical solution and simulations using the HYDRUS-1D software package. Results obtained with the proposed method were far less dependent upon the grid spacing than the HYDRUS-1D finite element solutions.
In the present paper, we develop an efficient and accurate numerical approach based on one-dimens... more In the present paper, we develop an efficient and accurate numerical approach based on one-dimensional-moving integrated radial basis function (1D-MIRBF) and fully implicit modified Picard method for simulating fluid movement in heterogeneous soils governed by the highly non-linear Richards equation. The major advantages of the proposed 1D-MIRBF method include (i) a banded sparse system matrix that helps reduce the computational cost; (ii) the Kronecker Delta property of the constructed shape functions, which helps impose the essential boundary conditions in an exact manner; and (iii) high accuracy and fast convergence rate owing to the use of the IRBF approximation. The performance of the present method is demonstrated through several 1--D and 2--D soil infiltration problems. Numerical results obtained are in agreement with other published results in the literature. This solver for moisture motion in soils will be incorporated into a surface-water-flow solver to handle the surface ...
We analyse a nonlinear partial differential equation modelling reaction-diffusion systems with no... more We analyse a nonlinear partial differential equation modelling reaction-diffusion systems with nonlocal coupling and reaction fronts of gasless combustion. The equation is of active-dissipative type, nonlinear, with 6th-order spatial derivative. To numerically solve the equations we use the one-dimensional integrated radial basis function network (1D-IRBFN)method. The method has been previously developed and successfully applied to several problems such as structural analysis, viscous and viscoelastic flows and fluid-structure interaction. A commonly used approach is to differentiate a function of interest to obtain approximate derivatives. However, this leads to a reduction in convergence rate for derivatives and this reduction is an increasing function of derivative order. Accordingly, differentiation magnifies errors. To avoid this problem and recognising that integration is a smoothing process, the proposed 1D-IRBFN method uses the integral formulation, where spectral approximan...
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020
In this paper, we investigate a wide range of dynamical regimes produced by the nonlinearly excit... more In this paper, we investigate a wide range of dynamical regimes produced by the nonlinearly excited phase (NEP) equation (a single sixth-order nonlinear partial differential equation) using a more advanced numerical method, namely, the integrated radial basis function network method. Previously, we obtained single-step spinning solutions of the equation using the Galerkin method. First, we verify the numerical solver through an exact solution of a forced version of the equation. Doing so, we compare the numerical results obtained for different space and time steps with the exact solution. Then, we apply the method to solve the NEP equation and reproduce the previously obtained spinning regimes. In the new series of numerical experiments, we find regimes in the form of spinning trains of steps/kinks comprising one, two, or three kinks. The evolution of the distance between the kinks is analyzed. Two different kinds of boundary conditions are considered: homogeneous and periodic. The ...
IOP Conference Series: Materials Science and Engineering, 2010
Page 1. Integrated-RBF network method for free vibration analysis of laminated composite plates T... more Page 1. Integrated-RBF network method for free vibration analysis of laminated composite plates This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2010 IOP Conf. Ser.: Mater. Sci. Eng. 10 012236 ...
International Journal for Numerical Methods in Fluids, 2012
SUMMARYThis paper presents a local moving least square‐one‐dimensional integrated radial basis fu... more SUMMARYThis paper presents a local moving least square‐one‐dimensional integrated radial basis function networks method for solving incompressible viscous flow problems using stream function‐vorticity formulation. In this method, the partition of unity method is employed as a framework to incorporate the moving least square and one‐dimensional integrated radial basis function networks techniques. The major advantages of the proposed method include the following: (i) a banded sparse system matrix which helps reduce the computational cost; (ii) the Kronecker‐ δ property of the constructed shape function which helps impose the essential boundary condition in an exact manner; and (iii) high accuracy and fast convergence rate owing to the use of integration instead of conventional differentiation to construct the local radial basis function approximations. Several examples including two‐dimensional (2D) Poisson problems, lid‐driven cavity flow and flow past a circular cylinder are consid...
Engineering Analysis With Boundary Elements, Oct 1, 2015
We propose a novel numerical approach based on incompressible smoothed particle hydrodynamics and... more We propose a novel numerical approach based on incompressible smoothed particle hydrodynamics and moving integrated radial basis function networks method, namely ISPH-MIRBFN, for solving incompressible viscous flow problems. In the ISPH method, the pressure is acquired from solving Poisson equation. In the present approach, the pressure Poisson equation is solved on a set of MIRBFN nodal points and the obtained results are then transferred to the SPH particles. The performance of the present method is investigated through several numerical examples including spin-down vortex, flows in a lid-driven closed-cavity and a lid-driven open-cavity with a prescribed bottom wall motion. Numerical results show that the proposed method reduces the spurious pressure fluctuations, yields a smoother pressure-field solution and maintains the computational efficiency when compared to the ISPH.
2021 ASABE Annual International Virtual Meeting, July 12-16, 2021
Abstract. This paper reports on the validation of two numerical approaches that were developed to... more Abstract. This paper reports on the validation of two numerical approaches that were developed to determine the effect of compaction on the soil water retention curve (WRC). The proposed approaches satisfactorily expanded the applicability of the van Genuchten (1980) model. In Approach 1, an optimization problem was solved to enable the van Genuchten model parameters α and η to be estimated for a range of soil bulk densities, based on the WRC of the corresponding non-compacted soil and the estimated saturation, residual, and permanent wilting-point (-1500 kPa) water contents of the compacted soil. In Approach 2, the parameter η was assumed to be unaffected by changes in soil bulk density. Subsequently, the parameter α was determined using an equation especially developed by this study. Compared with measured data, Approach 2 yielded slightly better predictions of the WRC than Approach 1. However, both numerical approaches may be used with confidence in a wider range of scenarios than those presented in this study. Across all soils, our analyses showed that relatively small increments in soil bulk density, due to compaction, can result in significant reductions in the available water storage capacity (AWSC) of soils; the effect being dependent on soil type and the relative increase in soil bulk density. Mechanization systems that mitigate, or where possible avoid, soil damage due to compaction (coupled with management practices that reduce loss of soil organic carbon) are encouraged. Quantification of the benefits of compaction avoidance, in terms of improved infiltration, soil water retention and water-use efficiency, as well as better predictions of the hydrology of compacted soils, may be possible through the application of the models reported in this study.
Abstract The machine acceleration introduced by H. J. Schulze has been a cornerstone of the bubbl... more Abstract The machine acceleration introduced by H. J. Schulze has been a cornerstone of the bubble-particle (BP) detachment theory. It connects the mean dissipation rate of turbulence energy of water in a flotation machine with the BP detachment. In a recent paper, we scrutinized the theory and recommended its extension to cover both the longitudinal (centrifugation) and transverse (shear) effects of water turbulence. Since there is a significant difference in the densities of water, solid particles, and air bubbles, it is unknown if the available determination of the machine acceleration using the “water particles” is a good approximation for the bubble-particle aggregates. This paper aims to provide an answer to this fundamental question. For simplicity, this paper focuses on the acceleration of solid particles in water. Specifically, we use the Basset-Boussinesq-Oseen equation to quantify the particle acceleration. The correlation method in combination with the isotropic turbulence theory is applied to predict the particle acceleration components for the full range of turbulence length scale. Comparing with Schulze’s model, our recent model shows that the particle inertia should be considered in calculating the machine acceleration, especially for large and/or heavy particles and high energy dissipation rate. Our numerical results show that the machine acceleration decreases with increasing particle size and density and increases with increasing dissipation rate of turbulent kinetic energy and turbulence intensity.
Abstract A new control volume approach is developed based on compact integrated radial basis func... more Abstract A new control volume approach is developed based on compact integrated radial basis function (CIRBF) stencils for solution of the highly nonlinear Richards equation describing transient water flow in variably saturated soils. Unlike the conventional control volume method, which is regarded as second-order accurate, the proposed approach has high-order accuracy owing to the use of a compact integrated radial basis function approximation that enables improved flux predictions. The method is used to solve the Richards equation for transient flow in 1D homogeneous and heterogeneous soil profiles. Numerical results for different boundary conditions, initial conditions and soil types are shown to be in good agreement with Warrick’s semi-analytical solution and simulations using the HYDRUS-1D software package. Results obtained with the proposed method were far less dependent upon the grid spacing than the HYDRUS-1D finite element solutions.
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