Link to math 536 site
Benchmark results for a 3D lid-driven cavity of size 1x1x2
My research interests can be summarized as follows.
For my CV and list of publications take a look here.
Here is also a collection of nice movies from our numerical simulations
This is a development of a shear layer instability.
This is a simulation of the sedimentation of two
64 spheres at Re=100,
and at Re=1.
Separation of 21 336 particles in a viscous liquid (direct simulation).
A single bubble at low Weber number.
Fluidized bed of 14,000 particles in a viscous liquid (direct simulation).
V. Calo, P. Minev, and V. Puzyrev, Splitting schemes for phase-field equations. Submitted to: Appl. Numer. Math.
P. Behnoudfara, V. Calo, Q. Deng, and P. Minev, A variationally separable splitting for the generalized-$\alpha$ method for parabolic equations. Published online at: Int. J. Numer. Meth. Engng. (2019).
J.L. Guermond and P. Minev, High-order adaptive time stepping for the Navier-Stokes equations. SIAM J. Sci. Comput., 41 (2019), A770-A788.
P. Minev, S. Srinivasan, and P. Vabishchevich, Flux formulation of parabolic equations with highly heterogeneous coefficients, J. Computational and Applied Mathematics, 340 (2018), 582-601.
P. Minev and P. Vabishchevich, Splitting schemes for the stress formulation of the incompressible Navier-Stokes equations, J. Computational and Applied Mathematics}, 344 (2018), 807-818.
P. Minev and P. Vabishchevich, Splitting schemes for unsteady problems involving the grad-div operator, Applied Numerical Mathematics, 124 (2018), 130-139.
J.L. Guermond and P. Minev, High-order time stepping for the Navier-Stokes equations with minimal computational complexity. J. Computational and Applied Mathematics, 310 (2017), 92–103.
J.L. Guermond and P. Minev, High-order time stepping for the incompressible Navier- Stokes equations. SIAM J. Sci. Comput., 37 (2015), A2656-A2681.
A. Roshchenko, P. Minev and W.H. Finlay, A Time Splitting Fictitious Domain Algorithm for Fluid-Structure Interaction Problems . J. Fluids and Structures, 58 (2015), 109– 126.
P. Minev, P. Vabishchevich, An operator-splitting scheme for the stream function–vorticity formulation of the unsteady Navier–Stokes equations. J. Computational and Applied Mathematics, 293 (2014), 147–163.
S. Madhavan, Y. Y. Al-Jahmany, P. D. Minev, and K. Nandakumar, On the transition to 3D modes for channel flow past a square cylinder. Canadian J. Chem. Eng., 92 (2014), 2122--2137.
T. Gornak, O. Iliev, P. Minev, A. Zemitis, A fast algorithm for 3D simulation of thermal stratification in containment pools of nuclear power plants. Computers&Mathematics with Applications, 67 (2014), 2228--2239.
T. Gornak, J.L. Guermond, O. Iliev, and P. Minev, A direction splitting approach for incompressible Brinkman flow. Int. J. Numer. Analysis Modeling, 4 (2013), 1--13.
J. Keating, P. Minev, A Fast Algorithm for Direct Simulation of Particulate Flows Using Conforming Grids. J. Comp. Phys. 255 (2013), 486--501.
J.L. Guermond, P. Minev, A. Salgado, Convergence Analysis of a Class of Massively Parallel Direction Splitting Algorithms for the Navier-Stokes Equations in Simple Domains. Math. Comp., 81 (2012), 1951--1977.
R.C. Marinez, A. Roshchenko, W.H. Finlay, P. D. Minev, Simulation of Enhanced Deposition due to Magnetic Field Alignment of Ellipsoidal Particles in a Lung Bifurcation. Journal of Aerosol Medicine and Pulmonary Drug Delivery, 25 (2012).
Ph. Angot, J. Keating, P. Minev, A Direction Splitting Algorithm for Incompressible Flow in Complex Geometries. Comp. Meth. Appl. Mech. Engng. 217 (2012), 111--120.
J.L. Guermond and P. Minev, Start-up flow in a three-dimensional lid-driven cavity by means of a massively parallel direction splitting algorithm. Int. J. Numer. Meth Fluids, 68 (2012), 856–-871.
A. Roshchenko, W.H. Finlay, P. D. Minev, The Aerodynamic Behaviour of Fibers in a Linear Shear Flow. Aerosol Sci. Tech., 45 (2011), 1260-1271.
J.L. Guermond and P. Minev, A new class of massively parallel direction splitting for the incompressible Navier-Stokes equations. Comp. Meth. Appl. Mech. Engng., 200 (2011), 2083--2093.
R Reddy, S Jin, K Nandakumar, PD Minev and J Joshi, DNS simulations of freely falling spheres: Effect of the surrounding particles on the settling velocity and drag coefficient. Int. J. CFD, 24 (2010) , 109 - 120.
JL Guermond and PD Minev, A new class of fractional step techniques for the incompressible Navier-Stokes equations using direction splitting. Compt. Rend. Acad. Sci., Mathematique, 348 (2010), 581-585.
C Huang, PD Minev, J Luo and K Nandakumar, A phenomenological model for erosion of material in a horizontal slurry pipeline flow. Wear, 269 (2010), 190-196.
R.K. Reddy, J.B. Joshi, K. Nandakumar, P. D. Minev, Direct numerical simulations of a freely falling sphere using fictitious domain method: Breaking of axisymmetric wake . Chem. Eng. Sci., 65 (2010), 2159-2171.
A. Dechaume, W. H. Finlay, P. D. Minev, A two-grid fictitious domain method for direct simulation of flows involving non-interacting particles of a very small size. Int. J. Numer. Meth Fluids, 63 (2010), 1241-1255.
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