Vani Cheruvu

	Vani Cheruvu

During FY2006 Vani Cheruvu (ASP postdoctoral fellow in IMAGe/Computational Mathematics Group) focused on two problems:

• Wavelet based limiting for discontinuous Galerkin method
• Development of spectral finite volume scheme for shallow water equations on the cubed-sphere

Motivation:

The high-order discontinuous Galerkin (DG) method is ideally suited for problems in atmospheric science due to its inherent nature of being conservative and easy incorporation of monotone slope limiters. Due to the lack of a good limiter, which is problem independent and within the framework of conservation principle, application of this method to atmospheric problems is restrictive.

This motivated her to work on developing wavelet based limiter for DG methods in collaboration with Dr. Jennifer Ryan (Asst. Professor, Dept. of Mathematics, Virginia Tech., Blacksburg, VA). Dr. Ryan submitted a proposal at Virginia Tech., for this research which got funded to train a graduate student in summer and travel funds for Vani to visit Virginia Tech. for collaborative research.

This also motivated her to consider Spectral Finite Volume method (SFV) for shallow water equations on cubed-sphere geometry. The advantage of SFV method over DG method is the ability to incorporate monotone limiters using flux-corrected transport (FCT) scheme. She, along with Dr. Nair and Dr. Tufo, developed SFV based transport model on the cubed-sphere.

Publications:

1. Vani Cheruvu, Ram D. Nair and Henry M. Tufo 2006: A Spectral Finite Volume Transport Scheme on the Cubed-Sphere, Applied Numerical Mathematics , in press.
2. Gregory Beylkin, Vani Cheruvu and Fernando Perez: Fast Adaptive Algorithms in the Non-Standard Form for Multidimensional Problems , Submitted to Journal of Computational Physics, 2006.
3. Vani Cheruvu and Jennifer Ryan: Wavelet based Limiter for discontinuous Galerkin Method, in preparation.

Presentations:

1. A nodal high-order spectral finite volume transport model on the cubed-sphere Poster Presentation, Scientific Computing Conference , Claremont, CA, November 2005.

(Support for this trip was from Harvey Mudd College, CA).

2. A nodal high-order spectral finite volume method for atmospheric modeling The 2006 Workshop on The Solution of Partial Differential Equations on the Sphere , Monterey, CA, June 26 - 29, 2006.

(Support for this trip was from Early Career Scientist Award, NCAR).

3. MRA based limiting for discontinuous Galerkin methods SIAM Annual Meeting , Boston, MA, July 10 - 14, 2006.

(Support for this trip was from Association for Women in Mathematics)

Participation:

Participated in Data Assimilation for the Carbon Cycle Summer Graduate Workshop , Mathematical Sciences Research Institute (MSRI), Berkeley, CA, July 17 - 28, 2006.

(Support for this trip is from MSRI & NCAR).

Education & Outreach :

One of the organizers of the event Weather and Climate: The Two Go Together for Girl Scouts at NCAR May & September 2006.

Service Work:

One of the co-ordinator for ASP Seminar Series 2005 - 2006.

This research, unless otherwise stated, is supported by the National Science Foundation.