Order Interpolation Scheme Research Articles

Numerical Analysis of Cavitation Using CIVA

We have developed a numerical method to evaluate behaviors of the cavitating bubbles based on the recent CFD (computational fluid dynamics) techniques. The method employs a finite-volume method combined with the high order and flexible interpolation scheme, CIVA. Two kinds of fluid behaviors, liquid (incompressible) and gas (compressible), are simultaneously computed by the unified scheme, CUP, which can handle the large density ratio (especially in case of mercury) associated with cavitation. By combining it with a new numerical cavitation model, which takes into account of compressibility of gas, good numerical results of water and mercury can be obtained._

Fine‐Scale Structures and Negative‐Density Regions: Comparison of Numerical Methods for Solving the Advection Equation

A common feature of the Vlasov equation is that it develops fine‐scale filamentation as time evolves, as observed, for example, in global nonlinear simulations of the ion‐temperature‐gradient instability. From a numerical point of view, it is not trivial to simulate nonlinear regimes characterized by increasingly smaller scales, which eventually become smaller than the (finite) grid size. When very small structures occur, higher order interpolation schemes have a tendency to produce overshoots and negative‐density regions unless some additional dissipative procedure is applied. Different interpolation schemes for the distribution function are compared and discussed.

CFD study of gas–solid behavior in downer reactors: An Eulerian–Eulerian approach

In this paper, a multiphase model applied to a downer reactor is proposed, where the gas–solid modeled with some special characteristics, such as: unsteady and 3D flow for two fluids on an Eulerian–Eulerian approach; dissipation of turbulent kinetic energy only on the gas phase modeled as real fluid; and the assumption that the solid phase behaves like a hypothetical fluid without shear stress from molecular causes. Studies based on first (HIPWIND) and second order (HIGHER UPWIND) interpolation schemes were carried out. The difference in the results using the two schemes was found to be negligible. The Computational Fluid Dynamic Technique (CFD) was adopted as a tool to predict downer reactor dynamic, comparing the proposed model with experimental data available in the literature. Good agreement between experimental data and model predictions was verified. Therefore CFD techniques proved to be a powerful tool to predict the fluid dynamic of inlet changing of downer reactors, and it can be used with success in chemical process optimization.

Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows: Part II: Multi-dimensional limiting process

Through the analysis of conventional TVD limiters, a new multi-dimensional limiting function is derived for an oscillation control in multi-dimensional flows. And, multi-dimensional limiting process (MLP) is developed with the multi-dimensional limiting function. The major advantage of MLP is to prevent oscillations across a multi-dimensional discontinuity, and it is readily compatible with more than third order spatial interpolation. Moreover, compared with other higher order interpolation schemes such as ENO type schemes, MLP shows a good convergence characteristic in a steady problem and it is very simple to be implemented. In the present paper, third and fifth order interpolation schemes with MLP, named MLP3 and MLP5, are developed and tested for several real applications. Through extensive numerous test cases including an oblique stationary contact discontinuity, an expansion fan, a vortex flow, a shock wave/vortex interaction and a viscous shock tube problem, it is verified that MLP combined with M-AUSMPW+ numerical flux substantially improves accuracy, efficiency and robustness both in continuous and discontinuous flows. By extending the current approach to three-dimensional flows, MLP is expected to reduce computational cost and enhance accuracy even further.

An effective high order interpolation scheme in BIEM for biharmonic boundary value problems

This paper presents an effective high order boundary integral equation method (BIEM) for the solution of biharmonic equations. All boundary values including geometries are approximated by high order radial basis function networks (RBFNs) rather than the conventional low order Lagrange interpolation schemes. For a better quality of approximation, the networks representing the boundary values and their derivatives are constructed by using integration processes. Prior conversions of network weights into nodal variable values are employed in order to form a square system of equations. Numerical results show that the proposed BIEM attains a great improvement in solution accuracy, convergence rate and computational efficiency over the linear- and quadratic-BIEMs.

Nearest-Grid-Point Interpolation in Gyrokinetic Particle-in-Cell Simulation

Linear interpolation or other higher order interpolation schemes are almost always used in particle-in-cell simulation because of their lower noise characteristics and accuracy relative to the nearest-grid-point method. The higher order interpolation schemes are chosen because of their optimal performance, balancing a smaller number of particles against more computer operations per particle per time step. However, this is not the case in large-scale gyrokinetic particle simulations, where sometimes nearest-grid-point interpolation is used with results virtually identical to those of linear interpolation using the same number of particles. Here, a comparison and analysis of nearest-grid-point and linear interpolation schemes is given showing why nearest-grid-point interpolation can be optimal. A simple two-dimensional slab model of the ion-temperature-gradient instability and associated generation of zonal flows is used to compare the interpolation schemes. Significant improvements in performance are possible by using nearest-grid-point interpolation because of the large number of gathers/scatters associated with gyroaveraging.

Error Analysis for the Interpolation-Supplemented Lattice-Boltzmann Equation Scheme

The numerical error of the interpolation-supplemented lattice-Boltzmann equation (ISLBE) scheme is theoretically analyzed. The ISLBE is proved to recover the Navier–Stokes equation as long as a second order interpolation scheme is used and the flow domain is appropriately discretized. Using a linear interpolation scheme will inevitably generate the numerical diffusivity and viscosity, making the ISLBE scheme unable to simulate the Navier–Stokes equation correctly. The analysis is consistent with previous numerical experiments.

Synthesis of absorbing boundary conditions for the FDTD method: numerical results

Presents numerical results in the form of a comparison of predictions due to a numerical algorithm using a previously published exact nonlocal absorbing boundary condition (ABC) and analytical results for the field radiated by an infinitely small dipole. The numerical approximations are derived, and application to the FDTD method is straightforward. The method is compared to a related approach due to De Moerlose et al., (see ibid., vol.41, no.7, p. 890-896, 1993) and it is shown that the method yields better accuracy since higher order interpolation and numerical integration schemes may be used with this formulation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>