Fluid Flow Simulation by Ming-Jun Lai

I used bivariate splines to simulate the air flows around two cars. See more fluid flow simulations in paper [16] listed below.

Ming-Jun Lai's Papers on Numerical PDE's

[17] G. Awanou and M. J. Lai, Trivariate Spline Approximations of 3D Navier-Stokes Equations , accepted for publication in Mathematics of Computation, 2004.

[16] M.J.Lai and P. Wenston, Bivariate Splines for Fluid Flows, Computers and Fluids 33(2004), pp. 1047--1073.

[15] M. J. Lai, Chun Liu, and Paul Wenston, On two nonlinear biharmonic evolution equations, accepted for publication in Applicable Analysis, 2003.

[14] M. J. Lai, Chun Liu, and Paul Wenston, Numerical simulation of two nonlinear biharmonic equations, accepted for publication in Applicable Analysis, 2003.

[13] M. J. Lai, Chun Liu, and Paul Wenston, Bivariate spline method for numerical solution of time evolution Navier-Stokes equations over polygons in stream function formulation, Numerical Methods for P. D. E., 2003 pp. 776--827.

[12] Bivariate splines for exterior biharmonic equations (with P. Wenston and L. A. Ying), in Approximation Theory X: Wavelets, Splines and Applications, edited by C. K. Chui, L. L. Schumaker, J. Stoeckler, Vanderbilt Univ. Press, 2002, pp. 385--404.

[11] The multivariate spline method for numerical solution of partial differential equations and scattered data interpolation (with G. Awanou and P. Wenston) , 2002.

[10] Trivariate $C^1$ cubic splines for numerical solution of biharmonic equations (with Paul Wenston), in: {\sl Trends in Approximation Theory}, K. Kopotun, T. Lyche, and M. Neamtu (eds.), Vanderbilt University Press, Nashville, 2001, pp. 224--234.

[9] Bivariate spline method for numerical solution of steady state Navier-Stokes equations over polygons in stream function formulation , (with Paul Wenston), in Advances in Computational Mathematics}, edited by Z. Chen, Y. Li, C. Micchelli, and Y. Xu, Marcel Dekker, New York, 1998, pp. 245--277.

[8] Bivariate Spline Method for Navier-Stokes Equations: Domain Decomposition Technique (with Paul Wenston), in Approximation Theory IX: Computational Aspects Charles K. Chui and Larry L. Schumaker (eds.) Vanderbilt University Press (Nashville), 1998, pp. 153--160.

[7] Two Nonlinear Biharmonic Evolution Equations Arising from the Study of Liquid Crystals, , (with Chun Liu and Paul Wenston), submitted.

[6] Bivariate spline method for numerical solution of time evolution Navier-Stokes equations over polygons in stream function formulation, (with Chun Liu and Paul Wenston), appear in Numer. Methods for PDE's, 2003.

[5] Bivariate spline method for numerical solution of the steady state Navier-Stokes equations over polygons in stream function formulation, (with Paul Wenston), Numer. Methods for PDE's, 16(2000), 147--183.

[4] Report on Numerical Experiments with Bivariate C^1 Cubic Splines for Numerical Solutions of Partial Differential Equations, (with Paul Wenston).

[3] Numerical approximation of diffusion equations over polygons using bivariate C^1 cubic splines, (with Paul Wenston).

[2] On Schwarz' domain decomposition methods for elliptic boundary value problems, (with Paul Wenston), Numer. Math. 84(2000), pp. 475-495.

[1] On multilevel bases for elliptic boundary value problems, (with Paul Wenston), Journal of Computational and Applied Mathematics, (71)1996, pp. 95--113.