SLADI: a semi-Lagrangian alternating-direction implicit method for the numerical solution of advection–diffusion problems with application to electricity storage valuations

2015 ◽  
Vol 19 (2) ◽  
pp. 69-108 ◽  
Author(s):  
Javier Hernández Ávalos ◽  
Paul. V Johnson ◽  
Peter W Duck
Keyword(s):  
Numerical Solution ◽  
Implicit Method ◽  
Alternating Direction Implicit Method ◽  
Alternating Direction Implicit ◽  
Electricity Storage ◽  
Advection Diffusion ◽  
Alternating Direction ◽  
Diffusion Problems

Issues related to the numerical simulation of herringbone grooved journal bearing including cavitation condition

2021 ◽  
pp. 135065012110625
Author(s):  
NV Borse ◽  
MA Sawant ◽  
SP Chippa
Keyword(s):  
Bulk Modulus ◽  
Numerical Solution ◽  
Journal Bearing ◽  
Load Capacity ◽  
Implicit Method ◽  
Time Step ◽  
Alternating Direction Implicit Method ◽  
Alternating Direction Implicit ◽  
Attitude Angle ◽  
Alternating Direction

This study aims to address the complexities involved in determining the numerical solution of herringbone grooved journal bearing considering cavitation. A modification is made to the Reynolds’ equation to include the effect of cavitation as given by Elrod's cavitation algorithm. Grid transformation is performed to consider the effect of the inclined grooves. The partial differential equation is discretised using finite-difference method. Then, the solution of the resulting set of equations is determined by the alternating-direction implicit method and the pressure, load capacity and attitude angle are obtained. Time step (Δ t) and Bulk modulus have a significant impact on the convergence of the numerical solution incorporating Elrod's cavitation algorithm. Use of alternating-direction implicit method over point by point method like Gauss–Seidel is essential to obtain convergence. Load capacity of the herringbone grooved journal bearing rises with the rise in eccentricity ratio. As compared to the Reynolds boundary conditions, Elrod's model results into lower attitude angle for herringbone grooved journal bearing. Cavitation distribution for herringbone grooved journal bearing is much lower than that of plain journal bearing. The effect of variation of groove angle on the herringbone grooved journal bearing's load capacity, side leakage and friction parameter is also determined. A detailed discussion on the various complexities such as treatment at groove ridge boundaries; numerical oscillations; choice of time step and bulk modulus; and influence of compressibility in the Couette term in full film region in the numerical analysis of herringbone grooved journal bearing specifically considering cavitation is given in this work. Multiple methods to deal with the aforementioned complexities are examined and appropriate solutions are obtained.

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