High Order Cubic-Polynomial Interpolation Schemes on Triangular Meshes

The Cubic-Polynomial Interpolation scheme has been developed and applied to many practical simulations.However,it seems the existing Cubic-Polynomial Interpolation scheme are restricted to uniform rectangular meshes.Consequently,this scheme has some limitations to problems in irregular domains.This paper will extend the Cubic-Polynomial Interpolation scheme to triangular meshes by using some spline interpolation techniques.Numerical examples are provided to demonstrate the accuracy of the proposed schemes.

Some Experiments with Multivariate Objective Analysis Scheme of Heights and Winds Using Optimum Interpolation

A two-dimensional, multitvariate objective analysis scheme for simultaneous analysis of geopotential height and wind fields has been developed over Indian and adjoining region for use in numerical weather prediction. The height-height correlations calculated using daily data of four July months (1976-1979), are used to derive the other autocorrelations and cross-correlations assuming geostropic relationship. A Gaussian function is used to model the autocorrelation function. Since the scheme is multivariate the regression coefficients (weights) are matrix.Near the equator, the geostrophic approximation relating mass and wind is decoupled in a way similar to Bergman (1979). The objective analyses were made over Indian and adjoining region for 850, 700, 500, 300 and 200 hPa levels for the period from 4 July to 8 July 1979, 12 GMT. The analyses obtained using multivariate optimum interpolation scheme depict the synoptic situations satisfactorily. The analyses were also compared with the FGGE analyses (from ECMWF) and also with the station observations by computing the root mean square (RMS) errors and the RMS errors are comparable with those obtained in other similar studies.

Multivariate Objective Analysis of Wind and Height Fields in the Tropics

The commollly used objective analysis scheme(Scheme-A) for the analysis Of wind and geopotential height smoothen the divergent component of the wind which is rather important in the tropics,specifically over convective regions.To overcome this deficiellcy, a new analysis SCheme in which divergent component is included in the statistical model of the wind forecast errors,has been proposed by Daley(1985).Following this scheme,a new set of correlahon functions of forecast errors for the indian region during monsoon season which are suitable for analysing the tropical wind are obtained.This analysis scheme(Scheme--B) as well as Scheme-A were used to make analyses for the period from 4 July to & July 1979(12 GMT) at 850,700 and 200 hpa levels over an area bounded by l.875'N to 39.375'N and 41.250'E to 108.750'E and subsequently divergent component,velocity potential are computed for both schemes.Results from both these schemes show that in the monsoon depression region the velocity potential and divergence have increased in the later case(Scheme-B).This suggests that the divergent component has been enhanced in Scheme-B and that the objechve of this study is realized to some extent.

ON TRIANGULAR C^1 SCHEMES: A NOVEL CONSTRUCTION

In this paper we present a C-1 interpolation scheme on a triangle. The interpolant assumes given values and one order derivatives at the vertices of the triangle. It is made up of partial interpolants blended with corresponding weight functions. Any partial interpolant is a piecewise cubics defined on a split of the triangle, while the weight function is just the respective barycentric coordinate. Hence the interpolant can be regarded as a piecewise quartic. We device a simple algorithm for the evaluation of the interpolant. It's easy to represent the interpolant with B-net method. We also depict the Franke's function and its interpolant, the illustration of which shows good visual effect of the scheme.

Generalized and Unified Families of Interpolating Subdivision Schemes

We present generalized and unified families of (2n)-point and (2n − 1)-point p-ary interpolating subdivision schemes originated from Lagrange polynomialfor any integers n ≥ 2 and p ≥ 3. Almost all existing even-point and odd-pointinterpolating schemes of lower and higher arity belong to this family of schemes. Wealso present tensor product version of generalized and unified families of schemes.Moreover error bounds between limit curves and control polygons of schemes arealso calculated. It has been observed that error bounds decrease when complexityof the scheme decrease and vice versa. Furthermore, error bounds decrease withthe increase of arity of the schemes. We also observe that in general the continuityof interpolating scheme do not increase by increasing complexity and arity of thescheme.

A NEW APPROACH TO THE SIMULATION OF UNSTEADY SUBCRITICAL FLOW

The use of the specified time interval numerical schemes has been popular in applying the method of characteristics to unsteady oped-channel flow problem. Studies and analyses of several variants of those schemes have led to the derivation of a complete set of timeline-interpolation scheme in applying the method of characteristics to Saint-Venant equations. A computer model based upon this scheme has ben successfully developed for predicting free surface unsteady flow, and has been verified by field experiment. Timeline interpolations, where the characteristic lines are projected back before the current time step,demonstrate much less damping than the corresponding spatial interpolation scheme at the same discretization.