Improving the precision of discrete numerical solutions using the generalized integral transform technique

2020 ◽  
Vol 42 (6) ◽  
Author(s):  
Isabela F. Pinheiro ◽  
Ricardo D. Santos ◽  
Leandro A. Sphaier ◽  
Leonardo S. de B. Alves
Keyword(s):  
Numerical Solutions ◽  
Integral Transform ◽  
Integral Transform Technique

scholarly journals Evaluation of hillslope storage with variable width under temporally varied rainfall recharge

2021 ◽  
Author(s):  
Ping-Cheng Hsieh ◽  
Tzu-Ting Huang
Keyword(s):  
Groundwater Flow ◽  
Analytical Solutions ◽  
Water Conservation ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Time Discretization ◽  
Third Order ◽  
Analytical And Numerical Solutions ◽  
Rainfall Recharge ◽  
Integral Transform Technique

Abstract. This study discussed water storage in aquifers of hillslopes under temporally varied rainfall recharge by employing a hillslope-storage equation to simulate groundwater flow. The hillslope width was assumed to vary exponentially to denote the following complex hillslope types: uniform, convergent, and divergent. Both analytical and numerical solutions were acquired for the storage equation with a recharge source. The analytical solution was obtained using an integral transform technique. The numerical solution was obtained using a finite difference method in which the upwind scheme was used for space derivatives and the third-order Runge–Kutta scheme was used for time discretization. The results revealed that hillslope type significantly influences the drains of hillslope storage. Drainage was the fastest for divergent hillslopes and the slowest for convergent hillslopes. The results obtained from analytical solutions require the tuning of a fitting parameter to better describe the groundwater flow. However, a gap existed between the analytical and numerical solutions under the same scenario owing to the different versions of the hillslope-storage equation. The study findings implied that numerical solutions are superior to analytical solutions for the nonlinear hillslope-storage equation, whereas the analytical solutions are better for the linearized hillslope-storage equation. The findings thus can benefit research on and have application in soil and water conservation.

Hybrid Analytical-Numerical Analysis of SAE 4150 Alloy Steel Rods Cooling

2014 ◽  
Vol 1082 ◽  
pp. 187-190 ◽  
Author(s):  
Marcelo Ferreira Pelegrini ◽  
Thiago Antonini Alves ◽  
Felipe Baptista Nishida ◽  
Ricardo A. Verdú Ramos ◽  
Cassio R. Macedo Maia
Keyword(s):  
Diffusion Equation ◽  
Alloy Steel ◽  
Integral Transform ◽  
Numerical Study ◽  
Physical Parameters ◽  
Analytical Treatment ◽  
Aspect Ratios ◽  
Rectangular Cylinders ◽  
Thermo Physical Properties ◽  
Integral Transform Technique

In this work, a hybrid analytical-numerical study was performed in cooling of rectangular rods made from SAE 4150 alloy steel (0.50% carbon, 0.85% chrome, 0.23% molybdenum, and 0.30% silicon). The analysis can be represented by the solution of transient diffusive problems in rectangular cylinders with variable thermo-physical properties in its domain under the boundary conditions of first kind (Dirichlet condition) and uniform initial condition. The diffusion equation was linearized through the Kirchhoff Transformation on the temperature potential to make the analytical treatment easier. The Generalized Integral Transform Technique (GITT) was applied on the diffusion equation in the domain in order to determine the temperature distribution. The physical parameters of interest were determined for several aspect ratios and compared with the results obtained through numerical simulations using the commercial software ANSYS/FluentTM15.

scholarly journals INTEGRAL TRANSFORM TECHNIQUE FOR MESON WAVE FUNCTIONS

1996 ◽  
Vol 11 (20) ◽  
pp. 1611-1626 ◽  
Author(s):  
A.P. BAKULEV ◽  
S.V. MIKHAILOV
Keyword(s):  
Wave Function ◽  
Sum Rules ◽  
Integral Transform ◽  
Wave Functions ◽  
Sum Rule ◽  
New Approach ◽  
Exactly Solvable ◽  
The Stability ◽  
The Masses ◽  
Integral Transform Technique

In a recent paper1 we have proposed a new approach for extracting the wave function of the π-meson φπ(x) and the masses and wave functions of its first resonances from the new QCD sum rules for nondiagonal correlators obtained in Ref. 2. Here, we test our approach using an exactly solvable toy model as illustration. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance (π′), but also in the estimation of π″-mass.

scholarly journals Analytical Solution of 1D Advection-Dispersion Equation In Finite Groundwater Reservoir With Spatially Dependent Dispersivity And Two Inputs Sources With Source-Sink Term Impact

2021 ◽  
Author(s):  
Thomas TJOCK-MBAGA ◽  
Patrice Ele Abiama ◽  
Jean Marie Ema'a Ema'a ◽  
Germain Hubert Ben-Bolie
Keyword(s):  
Analytical Solution ◽  
Linear Function ◽  
Dispersion Equation ◽  
Source Term ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Liouville Problem ◽  
Finite Domain ◽  
Advection Dispersion ◽  
Sink Term

Abstract This study derives an analytical solution of a one-dimensional (1D) advection-dispersion equation (ADE) for solute transport with two contaminant sources that takes into account the source term. For a heterogeneous medium, groundwater velocity is considered as a linear function while the dispersion as a nth-power of linear function of space and analytical solutions are obtained for and . The solution in a heterogeneous finite domain with unsteady coefficients is obtained using the Generalized Integral Transform Technique (GITT) with a new regular Sturm-Liouville Problem (SLP). The solutions are validated with the numerical solutions obtained using MATLAB pedpe solver and the existing solution from the proposed solutions. We exanimated the influence of the source term, the heterogeneity parameters and the unsteady coefficient on the solute concentration distribution. The results show that the source term produces a solute build-up while the heterogeneity level decreases the concentration level in the medium. As an illustration, model predictions are used to estimate the time histories of the radiological doses of uranium at different distances from the sources boundary in order to understand the potential radiological impact on the general public.

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