Node-centered Finite Volume Method Research Articles

Computational Analysis for Unsteady and Steady Magnetohydrodynamic Radiating Nano Fluid Flow past a Slippery Stretching Sheet Immersed in a Permeable Medium

This work gives an account of unsteady and steady radiating magnetohydrodynamics (MHD) nanofluid flow over a slippery stretching sheet embedded in a porous medium. A widely used similarity variables of such flows reduces a governing partial differential equations (PDEs) into a new set of partial differential equations (PDEs) in which a dependent variable is a function of two independent variables rather than three. At the same time, third order PDEs are converted into a second order PDEs by defining a new variable wherever it is deemed necessary. For the time integration, we perform first order explicit Euler method and spatial derivatives are approximated by the finite difference formulas in the context of node-centered finite volume method. It is revealed that for the unsteady flow the temperature of the nanofluid is higher near the surface without thermophoresis parameter Nt and reduced significantly when Nt is present. We also show that the concentration boundary layer thickness decreases with an increase of Darcy number Da.

A node-centered finite volume method for a fracture model on triangulations

In this paper, a node-centered finite volume method based on triangulations for a fracture model is presented, in which we restrict the pressure to the linear finite element space while the velocity can be approximated by constant vectors element by element. The numerical scheme is established just associated with the pressure to avoid the saddle-point problem. Error estimates of O(h) accuracy for the discrete H1 semi-norm and the discrete L2 norm of pressure p and the (L2)2 norm of velocity u are developed on general triangulations. Under an additional assumption about essentially symmetric control volumes, the error estimates for the pressure p can be improved to O(h3/2). Finally, numerical experiments are carried out to verify the accuracy and convergence rates for the proposed finite volume scheme.

Cell-centered high-order hyperbolic finite volume method for diffusion equation on unstructured grids

We apply a hyperbolic cell-centered finite volume method to solve a steady diffusion equation on unstructured meshes. This method, originally proposed by Nishikawa using a node-centered finite volume method, reformulates the elliptic nature of viscous fluxes into a set of augmented equations that makes the entire system hyperbolic. We introduce an efficient and accurate solution strategy for the cell-centered finite volume method. To obtain high-order accuracy for both solution and gradient variables, we use a successive order solution reconstruction: constant, linear, and quadratic (k-exact) reconstruction with an efficient reconstruction stencil, a so-called wrapping stencil. By the virtue of the cell-centered scheme, the source term evaluation was greatly simplified regardless of the solution order. For uniform schemes, we obtain the same order of accuracy, i.e., first, second, and third orders, for both the solution and its gradient variables. For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes. In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

A numerical scheme for coastal morphodynamic modelling on unstructured grids

Over the last decade, modelling systems based on unstructured grids have been appearing increasingly attractive to investigate the dynamics of coastal zones. However, the resolution of the sediment continuity equation to simulate bed evolution is a complex problem which often leads to the development of numerical oscillations. To overcome this problem, addition of artificial diffusion or bathymetric filters are commonly employed methods, although these techniques can potentially over-smooth the bathymetry. This study aims to present a numerical scheme based on the Weighted Essentially Non-Oscillatory (WENO) formalism to solve the bed continuity equation on unstructured grids in a finite volume formulation. The new solution is compared against a classical method, which combines a basic node-centered finite volume method with artificial diffusion, for three idealized test cases. This comparison reveals that a higher accuracy is obtained with our new method while the addition of diffusion appears inappropriate mainly due to the arbitrary choice of the diffusion coefficient. Moreover, the increased computation time associated with the WENO-based method to solve the bed continuity equation is negligible when considering a fully-coupled simulation with tides and waves. Finally, the application of the new method to the pluri-monthly evolution of an idealized inlet subjected to tides and waves shows the development of realistic bed features (e.g. secondary flood channels, ebb-delta sandbars, or oblique sandbars at the adjacent beaches), that are smoothed or nonexistent when using additional diffusion.

Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

AbstractWe couple a node-centered finite volume method to a high order finite difference method to simulate dynamic earthquake ruptures along nonplanar faults in two dimensions. The finite volume method is implemented on an unstructured mesh, providing the ability to handle complex geometries. The geometric complexities are limited to a small portion of the overall domain and elsewhere the high order finite difference method is used, enhancing efficiency. Both the finite volume and finite difference methods are in summation-by-parts form. Interface conditions coupling the numerical solution across physical interfaces like faults, and computational ones between structured and unstructured meshes, are enforced weakly using the simultaneous-approximation-term technique. The fault interface condition, or friction law, provides a nonlinear relation between fields on the two sides of the fault, and allows for the particle velocity field to be discontinuous across it. Stability is proved by deriving energy estimates; stability, accuracy, and efficiency of the hybrid method are confirmed with several computational experiments. The capabilities of the method are demonstrated by simulating an earthquake rupture propagating along the margins of a volcanic plug.

Eigensolutions of the Wigner–Eisenbud problem for a cylindrical nanowire within finite volume method

We present a node-centered finite volume method for computing a representative range of eigenvalues and eigenvectors of the Schrödinger operator on a three-dimensional cylindrically symmetric bounded domain with mixed boundary conditions. The three-dimensional Schrödinger operator is reduced to a family of two-dimensional Schrödinger operators distinguished by a centrifugal potential. We consider a uniform, boundary conforming Delaunay mesh, which additionally conforms to the material interfaces. We study how the anisotropy of the effective mass tensor acts on the uniform approximation of the first K eigenvalues and eigenvectors and their sequential arrangement. There exists an optimal uniform Delaunay discretization with matching anisotropy with respect to the effective masses of the host material. For a centrifugal potential one retrieves the theoretically established first-order convergence, while second-order convergence is recovered only on uniform grids with an anisotropy correction.

A Fully Adaptive Multiresolution Algorithm for Atrial Arrhythmia Simulation on Anatomically Realistic Unstructured Meshes

Biophysically detailed and anatomically realistic atrial models are emerging as a valuable tool in the study of atrial arrhythmias, nevertheless clinical use of these models would be favored by a reduction of computational times. This paper introduces a novel adaptive mesh algorithm, based on multiresolution representation (MR), for the efficient integration of cardiac ordinary differential equation (ODE)-partial differential equation (PDE) systems on unstructured triangle meshes. The algorithm applies a dynamically adapted node-centered finite volume method (FVM) scheme for integration of diffusion. The method accuracy and efficiency were evaluated by simulating propagation scenarios of increasing complexity levels (pacing, stable spirals, atrial fibrillation) on tomography-derived three-dimensional monolayer atrial models, based on a monodomain reaction-diffusion formulation coupled with the Courtemanche atrial ionic model. All simulated propagation patterns were accurately reproduced with substantially reduced computational times (10%-30% of the full-resolution simulation time). The proposed algorithm, combining the MR computational efficiency with the geometrical flexibility of unstructured meshes, may favor the development of patient-specific multiscale models of atrial arrhythmias and their application in the clinical setting.

242 カルマン渦放出周波数の格子依存性(S41-1 移動境界・連成(1),S41 移動境界・連成・振動と騒音問題)

Karman vortex sheets from a two dimensional circular cylinder at low Reynolds number are calculated using node-centered Finite Volume Method and unstructured mesh. In order to prepare for a coupling analysis between flow and structure oscillation, dependence of mesh density for frequency of vortex shedding are investigated in this paper. The results show that it is possible to capture a periodic vortex shedding using a sufficient quantity of unstructured hybrid mesh (mixture of prism and hexagon mesh).

Finite volume methods, unstructured meshes and strict stability for hyperbolic problems

The unstructured node centered finite volume method is analyzed and it is shown that it can be interpreted in the framework of summation by parts operators. It is also shown that introducing boundary conditions weakly produces strictly stable formulations. Numerical experiments corroborate the analysis.

Investigation of ionized fields due to bundled unipolar DC transmission lines in the presence of wind

The ionized fields of bundled unipolar DC power transmission lines are analysed by using an upwind node-centered finite volume method (FVM) based algorithm recently introduced by the authors. Geometric configurations considered are typical of practical DC lines and the effect of wind is included. The validity of the equivalent single conductor model in the presence of wind is verified.

UNSTRUCTURED GRID FINITE VOLUME ANALYSIS FOR ACOUSTIC AND PULSED WAVE PROPAGATION CHARACTERISTICS IN EXHAUST SILENCER SYSTEMS

The unstructured grid finite volume method has been applied to predict the linear and nonlinear attenuation characteristics of the expansion chamber type silencer system. In order to achieve grid flexibility and a solution adaptation for geometrically complex flow regions associated with the actual silencers, the unstructured mesh algorithm in context with the node-centered finite volume method has been employed. The validation cases for the linear and nonlinear wave propagation characteristics include the acoustic field of the concentric expansion chamber and the axisymmetric blast flow field with the open end. Effects of the chamber geometry on the nonlinear wave propagation characteristics are discussed in detail.