Flow Physics Lab - Research Interests

Part of the PhD research work by Shivakumar Kandre is published in the Fluid Dynamics Research (FDR), https://doi.org/10.1088/1873-7005/ad1dc0

Lattice Boltzmann Method (LBM): LBM started in early 1990's, is a computer simulation approach for complex fluid flow systems and has growing interests from researchers in computational multi-physics field. Unlike the traditional CFD methods, which numerically solve the conservation equations describing macroscopic properties (e.g., mass, momentum, energy), LBM models the fluid-flow with a statistical particle distribution functions (single particle description in phase-space and time), and this algorithm performs consecutive propagation and collision processes over a discrete lattice mesh. Due to its locality of the dynamics and only near-neighbour shifts of distributions, LBM has several advantages over other CFD methods, especially in dealing with complex boundaries, incorporating of microscopic interactions for multi-physics flow problems, and scalability with high performance computing on CPUs and GPUs. The lattice Boltzmann equation is a discrete-velocity Boltzmann equation and hence susceptible to lose some features of the full Boltzmann equation from kinetic theory due to the use of only a finite set of lattice velocities. [Ref. Lallemand, P., & Luo, L.S. (2000). Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability. Physical Review E, 61(6), 6546; Benzi, R., Succi, S., & Vergassola, M. (1992). The lattice Boltzmann equation: theory and applications. Physics Reports, 222(3), 145-197].

Finite Volume Method (FVM) and High-Resolution Schemes: High-resolution schemes are used in the numerical solution of partial differential equations where high accuracy is required in the presence of shocks or discontinuities. High-resolution schemes often use flux/slope limiters to limit the gradient around shocks or discontinuities. A particularly successful high-resolution scheme is the MUSCL (Monotonic Upwind Scheme for Conservation Laws) scheme which uses state extrapolation and limiters to achieve good accuracy. [Ref. Harten, A. (1983). High resolution schemes for hyperbolic conservation laws. Journal of computational physics, 49(3), 357-393; Sweby, P. K. (1984). High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM journal on numerical analysis, 21(5), 995-1011.Kawai, S., & Terashima, H. (2011). A high‐resolution scheme for compressible multicomponent flows with shock waves. International Journal for Numerical Methods in Fluids, 66(10), 1207-1225].

Phase-field Method (PF): Interfacial numerical problems, e.g. oil-water emulsions, phase-change are solved using PF method. The method is well-studied and applied to analyse solidification problems (under the driving force of undercooling) or phase-separation (influenced by supersaturation). The formulation is based on the free energy functional constructed using a phase order parameter. This is a diffuse interface approach. [Ref. Warren, J. A., & Boettinger, W. J. (1995). Prediction of dendritic growth and micro segregation patterns in a binary alloy using the phase-field method. Acta Metallurgica et Materialia, 43(2), 689-703].

Level-Set Method (LS): This method is used to tract the interfaces and interfacial dynamics. The level set function is advected in time with a normal velocity. Due to the numerical discretization of the advection equation, an artificial diffusion is introduced and certain corrections are necessary on the next time-step evoled level-set field. This method is applied using ghost-fluid approach for the interface jump conditions in order to simulate high-density, high-viscosity two-phase problems. [Ref. Sethian, J. A. (1996). A fast marching level set method for monotonically advancing fronts. Proceedings of the National Academy of Sciences, 93(4), 1591-1595; Peng, D., Merriman, B., Osher, S., Zhao, H., & Kang, M. (1999). A PDE-based fast local level set method. Journal of Computational Physics, 155(2), 410-438].

Discrete Element Method (DEM): A collection of particles (spherical/non-spherical) are tracked for their instantaneous positions, velocities and accelerations. A contact mechanics is solved using spring-dashpot type of system. The Newton's laws of motion are integrated using e.g. velocity verlet algorithm. DEM is becoming widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, and rock mechanics. [Yu, A. B. (2004). Discrete element method: An effective way for particle scale research of particulate matter. Engineering Computations, 21(2/3/4), 205-214].

Multigrid Technique (MG): This technique uses a hierarchy of discretizations while numerically solving the differential equations. The instantaneous solutions are transferred successively from fine mesh discretization to the coarse mesh with point-wise injections and then vice a versa using prolongation operations. The MG technique is used to accelerate convergence of an algorithm and is widely used in the traditionally CFD and recently being applied with LB methodology for fluid flow simulations. [Stüben, K., & Trottenberg, U. (1982). Multigrid methods: Fundamental algorithms, model problem analysis and applications (pp. 1-176). Springer Berlin Heidelberg].

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