Research Interests:

  • Numerical Methods based on Conservation Laws:-
  1. LDG Approaches for Diffusion Problems 
  2. Monotonic Limiting
  • Finite Volume Methods (Eulerian and Lagrangian)
  • High-Order Methods,  High-Performance Computing


 Shallow Water Model Simulations (Movies) on the Cubed-Sphere
                         with the 
Discontinuous Galerkin Method


       
cs-cube-color.jpgThe  physical domain (planet Earth) is a Cubed-Sphere, which is  obtained by the  equiangular central projection (or gnomonic) of an inscribed cube. This results in a non-orthogonal cuvilinear coordinate system on the surface of the sphere. However, the computational domain is a Cube with sides ranging from -pi/4 to +pi/4, and has a unifrom grid resolution.
The HOMME framewrok is designed on such a grid system.


1.) Scalar Advection of a Cosine Bell (Williamson Test Case-1)

                     Cosine_bell.jpg

2.) Deformational flow with  Moving  Vortices for Advection Problems 

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A New Benchmark Deformational Test

The moving vortices on the sphere are created with a combination of solid-body rotational and deformational flow fields on the surface of the sphere. The dual vortices will be generated at dimetrically opposite positions on the sphere. The flow is time dependent, non-divergent, and the anlytic solution is known at any  given time. The flow orientation can be controlled by a parameter which directs the flow in any direction along a great-circle.  This test can be used for any type of spherical grids.

More details of this test can be found in
 Nair & Jablonowski (2008).
                     

3.) Flow Over an Isolated Mountain (Williamson SW Test Case-5)

                       sw5_icon


         
        4.) Rossby-Haurwitz Waves (SW Test Case-6)


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