Name
Abstract | ||
|---|---|---|
The numerical accuracy of the Interpolated Differential Operator (IDO) scheme is studied with Fourier analysis for the solutions of Partial Differential Equations (PDEs): advection, diffusion, and Poisson equations. The IDO scheme solves governing equations not only for physical variable but also for first-order spatial derivative. Spatial discretizations are based on Hermite interpolation functions with both of them. In the Fourier analysis for the IDO scheme, the Fourier coefficients of the physical variable and the first-order derivative are coupled by the equations derived from the governing equations. The analysis shows the IDO scheme resolves all the wavenumbers with higher accuracy than the fourth-order Finite Difference (FD) and Compact Difference (CD) schemes for advection equation. In particular, for high wavenumbers, the accuracy is superior to that of the sixth-order Combined Compact Difference (CCD) scheme. The diffusion and Poisson equations are also more accurately solved in comparison with the FD and CD schemes. These results show that the IDO scheme guarantees highly resolved solutions for all the terms of fluid flow equations. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.jcp.2006.01.015 | J. Comput. Physics |
Keywords | Field | DocType |
numerical accuracy,high resolution,computational fluid dynamics,02.70.rw,fourier coefficient,numerical stability,poisson equation,ido scheme,physical variable,cd scheme,fourth-order finite difference,accuracy study,fourier analysis,02.60.−x,02.60.cb,compact difference,higher accuracy,first order,hermite interpolation,differential operators,fluid flow,finite difference,partial differential equation | Discretization,Fourier analysis,Poisson's equation,Mathematical analysis,Finite difference,Fourier series,Partial differential equation,Hermite interpolation,Mathematics,Numerical stability | Journal |
Volume | Issue | ISSN |
217 | 2 | Journal of Computational Physics |
Citations | PageRank | References |
3 | 0.65 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yohsuke Imai | 1 | 12 | 2.80 |
| Takayuki Aoki | 2 | 188 | 17.87 |