Research Interests

• • Adaptive and Hybrid Modelling
    As simulations are being applied to more and more complex applications, conventional simulations methods tend to become very expensive (in terms of both resources and time required) to accurately model the physical phenomenon on interest. A key idea to fix this is to adaptively choose how detailed the mathematical and computational models need to be. This involves changing the amount of detail used during a simulation, by adapting it in both space and time.

    A key area of my research focus is to develop adaptive methods to solve this issue. My work in this direction can be classified into two directions:

    > H-adaptivity : This involves adaptively changing the mesh(or meshfree) resolution using error indicators and estimators.
    > Model adaptivity : This involves adaptively changing the governing equations and boundary conditions. For this, we use two different computational models to model the same material, and adaptively choose where to apply which model in space and time. They key goal here is to couple the two models, and transition between them, without any a-priori information about which model to use where.
    We are currently using idea to combine thin film flow and bulk flow models.

• • Computational Fluid Dynamics
    CFD has been shown to be a very useful tool in understanding various transport phenomena in both science and industry.
    My work focuses on free surface liquid flows, with a special emphasis on industry relevant flow problems. My work covers:
    

    > Thin film flow
    > Phase change using one-fluid models for both thin film and bulk flow
    > Multi-phase flow
    > Particle-laden flow
    > Water and fluid management in the automotive industry

• • Meshfree and Particle Methods
    Meshfree and particle-based methods have been shown to be a very useful alternative to conventional mesh-based methods when the computational domain undergoes large deformations and displacements. These methods becomes especially relevant in the presence of free surfaces and moving interfaces.

    A key portion of my research focuses on the development of meshfree and particle methods, understanding and trying to overcome their drawbacks, with a special emphasis on fluid flow applications. My work in meshfree methods includes:

    > Conservation in meshfree methods for fluid flow
    > Point cloud generation for domain discretization
    > Adaptive mesh(free) refinement
    > From CAD to Point Clouds
    > Meshfree Generalized Finite Difference Methods (GFDM)
    > Meshfree methods for surface PDEs