Finite Volume Method for Time-Dependent Convection Diffusion Large Reynolds Number Problem

An unstructured triangular mesh is successfully applied to the static simulations of air bearing sliders due to its flexibility, accuracy and mesh efficiency in capturing various complex rails and recess wall regions of air bearing surface, as well as fast simulation speed. This paper introduces a new implicit algorithm with second order time accuracy for the time-dependent simulations of the slider dynamics and available for the unstructured triangular mesh. The new algorithm is specially developed for the finite volume method. Since the algorithm has second order time accuracy, it provides the flexibility of applying various time steps while guaranteeing the numerical accuracy and convergence. Moreover, the unstructured triangular mesh is highly efficient and fewer nodes are used. Finally, due to the small variation of flying attitude between two neighboring time steps, it is especially efficient for iteration methods which are used in the finite volume method. As a result, the algorithm shows very fast speed in time-dependent dynamic simulations. Simulation studies are conducted on the flying dynamics of a thermal flying-height control slider after external excitations. The simulation results are compared with the simulation results obtained by the rectangular mesh based on the finite element method. It is observed that the simulation results are well correlated. The fast Fourier transform is also employed to analyze the air bearing frequencies. It is indicated that the new algorithm is of high efficiency and importance for time-dependent dynamic simulations.

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Block-preconditioners for the incompressible Navier–Stokes equations discretized by a finite volume method

Journal of Numerical Mathematics ◽

10.1515/jnma-2015-0120 ◽

2017 ◽

Vol 25 (2) ◽

Cited By ~ 3

Author(s):

Xin He ◽

Cornelis Vuik ◽

Christiaan Klaij

Keyword(s):

Reynolds Number ◽

Finite Volume Method ◽

Finite Volume ◽

Augmented Lagrangian ◽

Dimensionless Parameter ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Optimal Value ◽

Volume Method

Abstract The modified augmented Lagrangian preconditioner has attracted much attention in solving nondimensional Navier–Stokes equations discretized by the finite element method. In industrial applications the governing equations are often in dimensional form and discretized using the finite volume method. This paper assesses the capability of this preconditioner for dimensional Navier–Stokes equations in the context of the finite volume method. Two main contributions are made. First, this paper introduces a new dimensionless parameter that is involved in the modified augmented Lagrangian preconditioner. Second, with a number of academic test problems this paper reveals that the convergence of both nonlinear and linear iterations depend on this dimensionless parameter. A way to choose the optimal value of the dimensionless parameter is suggested and it is found that the optimal value is dependent of the Reynolds number, instead of the fluid’s properties, e.g., density and dynamic viscosity. The outcomes of this paper yield a potential rule to choose the optimal dimensionless parameter in practice, namely, correspondingly increasing with enlarging the Reynolds number.

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