arXiv subjects

Ravi Samtaney

Publications and source records attributed to Ravi Samtaney.

27 records · Page 2Linked to original sources

arXiv2018

Flow Past a Circular Cylinder on Curved Surfaces

We investigate the dynamics of flows past a stationary circular cylinder embedded on spherical and cylindrical surfaces at a fixed Reynolds number of 100. For flows on surfaces, it is convenient to express the Navier-Stokes equations in exterior calculus notation. We employ the discrete exterior calculus (DEC) method (Mohamed et al. (2016)) to numerically solve the equations. We explore the role played by curvature on dynamical quantities of interest: the drag coefficient (Cd), the lift coefficient (Cl), and the Strouhal number (St). Our simulations indicate that the effect of surface curvature on these quantities and the overall flow dynamics is somewhat insignificant thereby implying that the dynamics of the flow past a stationary circular cylinder exhibits universality, independent of the embedding surface geometry.

physics.flu-dyn↗

arXiv2018

Scaling of a Fast Fourier Transform and a Pseudo-spectral Fluid Solver up to 196608 cores

In this paper we present scaling results of a FFT library, FFTK, and a pseudospectral code, Tarang, on grid resolutions up to $8192^3$ grid using 65536 cores of Blue Gene/P and 196608 cores of Cray XC40 supercomputers. We observe that communication dominates computation, more so on the Cray XC40. The computation time scales as $T_\mathrm{comp} \sim p^{-1}$, and the communication time as $T_\mathrm{comm} \sim n^{-γ_2}$ with $γ_2$ ranging from 0.7 to 0.9 for Blue Gene/P, and from 0.43 to 0.73 for Cray XC40. FFTK, and the fluid and convection solvers of Tarang exhibit weak as well as strong scaling nearly up to 196608 cores of Cray XC40. We perform a comparative study of the performance on the Blue Gene/P and Cray XC40 clusters.

physics.comp-ph↗

arXiv2018

Numerical Convergence of Discrete Exterior Calculus on Arbitrary Surface Meshes

Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special (Delaunay) triangulations, which complicated the mesh generation process especially on curved surfaces. This paper presents numerical evidences demonstrating that this restriction is unnecessary. Convergence experiments are carried out for various physical problems using both Delaunay and non-Delaunay triangulations. Signed diagonal definition for the key DEC operator (Hodge star) is adopted. The errors converge as expected for all considered meshes and experiments. This relieves the DEC paradigm from unnecessary triangulation limitation.

math.NA↗

arXiv2016

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

physics.flu-dyn↗

arXiv2015

Energy transfers in dynamos with small magnetic Prandtl numbers

We perform numerical simulation of dynamo with magnetic Prandtl number $\mathrm{Pm} =0.2$ on $1024^3$ grid, and compute the energy fluxes and the shell-to-shell energy transfers. These computations indicate that the magnetic energy growth takes place mainly due to the energy transfers from large-scale velocity field to large-scale magnetic field and that the magnetic energy flux is forward. The steady-state magnetic energy is much smaller than the kinetic energy, rather than equipartition; this is because the magnetic Reynolds number is near the dynamo transition regime. We also contrast our results with those for dynamo with $\mathrm{Pm} =20$ and decaying dynamo.

physics.flu-dyn↗

arXiv2014

Non-modal stability analysis and transient growth in a magnetized Vlasov plasma

Collisionless plasmas, such as those encountered in tokamaks, exhibit a rich variety of instabilities. The physical origin, triggering mechanisms and fundamental understanding of many plasma instabilities, however, are still open problems. We investigate the stability properties of a collisionless Vlasov plasma in a stationary homogeneous magnetic field. We narrow the scope of our investigation to the case of Maxwellian plasma. For the first time using a fully kinetic approach we show the emergence of the local instability, a transient growth, followed by classical Landau damping in a stable magnetized plasma. We show that the linearized Vlasov operator is non-normal leading to the algebraic growth of the perturbations using non-modal stability theory. The typical time scales of the obtained instabilities are of the order of several plasma periods. The first-order distribution function and the corresponding electric field are calculated and the dependence on the magnetic field and perturbation parameters is studied. Our results offer a new scenario of the emergence and development of plasma instabilities on the kinetic scale.

physics.plasm-ph↗

arXiv2014

Energy transfers and magnetic energy growth in small-scale dynamo

In this letter we investigate the dynamics of magnetic energy growth in small-scale dynamo by studying energy transfers, mainly energy fluxes and shell-to-shell energy transfers. We perform dynamo simulations for magnetic Prandtl number $\mathrm{Pm}=20$ on $1024^3$ grid using pseudospectral method. We demonstrate that the magnetic energy growth is caused by nonlocal energy transfers from the large-scale or forcing-scale velocity field to small-scale magnetic field. The peak of these energy transfers move towards lower wavenumbers as dynamo evolves, which is the reason why the integral scale of the magnetic field increases with time. The energy transfers $U2U$ (velocity to velocity) and $B2B$ (magnetic to magnetic) are forward and local.

physics.flu-dyn↗

arXiv2012

A low memory, highly concurrent multigrid algorithm

We examine what is an efficient and scalable nonlinear solver, with low work and memory complexity, for many classes of discretized partial differential equations (PDEs) - matrix-free Full multigrid (FMG) with a Full Approximation Storage (FAS) - in the context of current trends in computer architectures. Brandt proposed an extremely low memory FMG-FAS algorithm over 25 years ago that has several attractive properties for reducing costs on modern - memory centric -- machines and has not been developed to our knowledge. This method, segmental refinement (SR), has very low memory requirements because the finest grids need not be held in memory at any one time but can be "swept" through, computing coarse grid correction and any quantities of interest, allowing for orders of magnitude reduction in memory usage. This algorithm has two useful ideas for effectively exploiting future architectures: improved data locality and reuse via "vertical" processing of the multigrid algorithms and the method of $τ$-corrections, which allows for not storing the entire fine grids at any one time. This report develops this algorithm for a model problem and a parallel generalization of the original sweeping technique. We show that FMG-FAS-SR can work as originally predicted, solving systems accurately enough to maintain the convergence rate of the discretization with one FMG iteration, and that the parallel algorithm provides a natural approach to fully exploiting the available parallelism of FMG.

math.NA↗

arXiv2012

Benchmarking and scaling studies of a pseudospectral code Tarang for turbulence simulations

Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh-Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on $1024^3$, $2048^3$, and $4096^3$ grids using the {\em HPC system} of IIT Kanpur and {\em Shaheen} of KAUST. We observe good "weak" and "strong" scaling for Tarang on these systems.

physics.comp-ph↗