Drop inertia, and one spends the rest of the project calibrating it back in. We keep it. We model urban floods, runoff, subsurface flow, and landslide-generated waves with depth-averaged solvers and Incompressible SPH, keeping every term we can afford and justifying every one we can't. We write our own codes. Also our own bugs. One who reads the equations before the manual will fit right in.

Study Domain

Solution of Shallow Water Equation (Left) and Diffusive Wave Equation (Right) with 2mm/hr rainfall pulses. Contour is given at the center.

Same rain. Same terrain. Same Manning's n. Different physics.

57600 cells and 40 minutes

12km X 12km, Sogam, Jammu and Kashmir, India

Shallow Water Equation

Elevation contours

Diffusive Wave Equation

06km X 06km, Kanpur, Uttar Pradesh, India

Shallow Water Equation

Elevation contours

Diffusive Wave Equation

Lead Developer: Naveed; Co-Developers: Ravi, Alok; Beta Tester: gourab

Simulation of idealized landslide induced waves. On the left hand there is granular column collapse, the corresponding waves generated in fluid are on the right. Granular column is simulated as Multilayered Depth-averaged Continuum with µ(I) rheology, whereas fluid is modelled using Incompressible Smoothed Particle Hydrodynamics (ISPH, at top) and Multilayered Shallow Water formulation (bottom). Colour represents velocity magnitude.

From top to bottom, the computational overhead decreases by 4! ...

Developer: Naveed; Beta Tester: gourab

Current

Ph.D.
- Alok Kumar (2020–)
- Ravi Shukla (2020–)

Completed

Post-Doc
- Naveed Ul Hassan Bhat (2025–2026)
Ph.D.
- Naveed Ul Hassan Bhat, 2025: Granular deformation coupled with fluid flow: multilayered depth-averaging
M.Tech
- Ramanjaneyulu, 2024: Experimental Study of Landslide Generated Impulse Waves in a Confined Water Body
- Preethan M C, 2024: Method of characteristics: Applications to Conduits, Free-Surface, and Sub-Surface Flows
- Naveed Ul Hassan Bhat, 2022: Diffusion Wave Approximation of Depth-averaged Flow Interaction with Porous Media (Best M.Tech Thesis 2022, Indian Society for Hydraulics)
- Alok Kumar, 2020: A Unified Depth-Averaged Approach for Integrated Modeling of Surface and Subsurface Flow Systems (Best M.Tech Thesis 2020, Indian Society for Hydraulics)
- Parth Singh Rajkumar, 2020: An Implicit 2D Zero-Inertia Model for Overland Flow

Shukla, R., Bhat, N., Kumar, A., Pahar, G., 2026. "Efficient and coupled 1D-2D hydrodynamic framework to model catchment scale surface flow dynamics" Journal of Hydrologic Engineering 31(6), 04026059-1-14.
Bhat, N., Ieja, R., Pahar, G., 2026. "Wave generation due to partially and completely submerged column collapse" ISH Journal of Hydraulic Engineering 32(3).
Bhat, N., Pahar, G., 2025. "Coupled ISPH-MFVM modeling of incompressible fluid-immiscible granular flow interaction" Computational Particle Mechanics 12, 4533-4565.
Bhat, N., Pahar, G., 2025. "A novel two component multilayered depth-averaged model for coupling fluid-granular systems" International Journal of Multiphase Flow 191, 105321.
Bhat, N., Pahar, G., 2025., "Multilayered depth-averaged formulation for immiscible gravity currents" Ocean Engineering 322, 120452.
Kumar, A., Pahar, G., 2024. "Macroscopic modeling of urban flood inundation through Areal-averaged Shallow-Water-Equations" Advances in Water Resources 190, 104755.
Bhat, N., Pahar, G., 2024. "Coupled ISPH Framework for Modeling Tsunamis Induced by Landslides: Sub-aerial to Submerged " Journal of Hydraulic Engineering 150(3), 04024009.
Bhat, N., Pahar, G., 2024. "Layered Shallow water Equations: Spatiotemporally varying layer ratios with specific adaptation to wet/dry interfaces" International Journal for Numerical Methods in Fluids 96(4), 397-434.
Bhat, N., Pahar, G., 2023. "Granular media deformation and fluid flow as overlapping, concurrent, coupled multilayered depth-averaged framework" Ocean Engineering 283, 114957.
Kumar, A., Pahar, G., 2023. "On Applicability of Dynamic, Local, And Diffusive Wave Models for Unified Depth-Averaged Fluid Flow Interaction With Porous Media" Journal of Hydrologic Engineering 28 (10), 4023028 1-13.
Bhat, N., Pahar, G., 2022. "Depth-averaged coupling of submerged granular deformation with fluid flow: An augmented HLL scheme" Journal of Hydrology, 606, 127364.
Bhat, N., Pahar, G., 2021. "Euler-Lagrange framework for deformation of granular media coupled with the ambient fluid flow" Applied Ocean Research, 116, 102857.
Bhat, N., Pahar, G., 2021. "Diffusion Wave Approximation of Depth-averaged Flow Interaction with Porous Media" Journal of Hydrologic Engineering, 26(2), 04020064.
Kumar, A., Pahar, G., 2020. "A Unified Depth-averaged Approach for Integrated Modeling of Surface and Subsurface Flow Systems" Journal of Hydrology, 591, 125339.
Pahar, G., Dhar, A., 2019. "On Information Coupling in Hybrid ISPH Framework for Fluidized Granular Systems" Advances in Water Resources, 131, 103366.
Pahar, G., Dhar, A., 2018. "On Modelling of MPS-based Multiphase Fluid Flow with Low Density Ratios" International Journal of Numerical Methods in Fluids, 87(10), 529-542.
Pahar, G., Dhar, A., 2018. "On Force Consideration in Coupled ISPH Framework for Sediment Transport in Presence of Free-surface Flow" Environmental Fluid Mechanics, 18(3), 555-579.
Pahar, G., Dhar, A., Islam, M. R. I., 2017. "Extending Incompressible SPH Framework for Simulation of Axisymmetric Free-surface Flows" Engineering Analysis with Boundary Elements, 84C, 35-41.
Pahar, G., Dhar, A., 2017. "On Modification of Pressure Gradient Operator in Integrated ISPH for Multifluid and Porous Media Flow with Free-surface" Engineering Analysis with Boundary Elements, 80C, 38-48.
Pahar, G., Dhar, A., 2017. "Numerical Modelling of Free-surface Flow-Porous Media interaction using Divergence-free Moving Particle Semi-Implicit Method" Transport in Porous Media, 118(2), 157-175.
Pahar, G., Dhar, A., 2017. "Coupled incompressible Smoothed Particle Hydrodynamics model for continuum-based modelling sediment transport" Advances in Water Resources, 102, 84-98.
Pahar, G., Dhar, A., 2017. "Robust boundary treatment for open-channel flows in divergence-free incompressible SPH" Journal of Hydrology, 546, 464-475.
Pahar, G., Dhar, A., 2016. "Mixed miscible-immiscible fluid flow modelling with incompressible SPH framework" Engineering Analysis with Boundary Elements, 73, 50-60.
Pahar, G., Dhar, A., 2016. "A Robust volume conservative divergence-free ISPH framework for free-surface flow problems" Advances in Water Resources, 96, 423-437.
Pahar, G., Dhar, A., 2016. "Modeling free-surface flow in porous media with modified incompressible SPH" Engineering Analysis with Boundary Elements, 68, 75-85.
Pahar, G., Dhar, A., 2014. "A dry zone-wet zone based modeling of surface water and groundwater interaction for generalized ground profile" Journal of Hydrology, 519 (Part B), 2215-2223.