arXiv subjects

Shuvam Sen

Publications and source records attributed to Shuvam Sen.

5 recordsLinked to original sources

arXiv2024

A new transient higher order compact scheme for computation of flow and heat transfer in nonuniform polar grids

In this work, a higher order compact (HOC) discretization is developed on the nonuniform polar grid. The discretization conceptualized using the unsteady convection-diffusion equation (CDE) is further extended to flow problems governed by the Navies-Stokes (N-S) equations as well as the Boussinesq equations. The scheme developed here combines the advantages of body-fitted mesh with grid clustering, thereby making it efficient to capture flow gradients on polar grids. The scheme carries a spatial convergence of order three with temporal order of convergence being almost two. Diverse flow problems are being investigated using the scheme. Apart from two verification studies we validate the scheme by time marching simulation for the benchmark problem of driven polar cavity and the problem of natural convection in the horizontal concentric annulus. In the process, a one-sided approximation for the Neumann boundary condition for vorticity is also presented. Finally, the benchmark problem of forced convection around a circular cylinder is tackled. The results obtained in this study are analyzed and compared with the well-established numerical and experimental data wherever available in the literature. The newly developed scheme is found to generate accurate solutions in each case.

physics.flu-dyn↗

arXiv2021

Fourth order compact scheme for the Navier-Stokes equations on time deformable domains

In this work, we report the development of a spatially fourth order temporally second order compact scheme for incompressible Navier-Stokes (N-S) equations in time-varying domain. Sen [J. Comput. Phys. 251 (2013) 251-271] put forward an implicit compact finite difference scheme for the unsteady convection-diffusion equation. It is now further extended to simulate fluid flow problems on deformable surfaces using curvilinear moving grids. The formulation is conceptualized in conjunction with recent advances in numerical grid deformations techniques such as inverse distance weighting (IDW) interpolation and its hybrid implementation. Adequate emphasis is provided to approximate grid metrics up to the desired level of accuracy and freestream preserving property has been numerically examined. As we discretize the non-conservative form of the N-S equation, the importance of accurate satisfaction of geometric conservation law (GCL) is investigated. To the best of our knowledge, this is the first higher order compact method that can directly tackle non-conservative form of N-S equation in single and multi-block time dependent complex regions. Several numerical verification and validation studies are carried out to illustrate the flexibility of the approach to handle high-order approximations on evolving geometries.

math.NA↗

arXiv2018

Phase error analysis of implicit Runge-Kutta methods: Introducing new classes of minimal dissipation low dispersion high order schemes

In current research, we analyse dissipation and dispersion characteristics of most accurate two and three stage Gauss-Legendre implicit Runge-Kutta (R-K) methods. These methods, known for their $A$-stability and immense accuracy, are observed to carry minimum dissipation error along with highest possible dispersive order in their respective classes. We investigate to reveal that these schemes are inherently optimized to carry low phase error only at small wavenumber. As larger temporal step size is imperative in conjunction with implicit R-K methods for physical problems, we interpret to derive a class of minimum dissipation and optimally low dispersion implicit R-K schemes. Schemes thus obtained by cutting down amplification error and maximum reduction of weighted phase error, suggest better accuracy for relatively bigger CFL number. Significantly, we are able to outline an algorithm that can be used to design stable implicit R-K methods for suitable time step with better accuracy virtues. The algorithm is potentially generalizable for implicit R-K class of methods. As we focus on two and three stage schemes a comprehensive comparison is carried out using numerical test cases.

math.NA↗

arXiv2013

Fourth order compact schemes for variable coefficient parabolic problems with mixed derivatives

In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth order spatial discretization. The time discretization has been carried out using using second order Crank-Nicolson. The present scheme shows good dispersion relation preserving property and has been thoroughly investigated for stability. The discrete Fourier analysis shows that the method is unconditionally stable. The fact that the method has been particularly developed for parabolic equations with mixed derivatives makes it suitable for solving incompressible Navier-Stokes (N-S) equations in irregular domains. To verify the proposed method, several problems with exact and benchmark solutions has been investigated. The proposed compact discretization has been extended to tackle flows of varying complexities governed by the two-dimensional unsteady N-S equations in domain beyond rectangular. The results show good agreement for all the problems considered.

math.NA↗

arXiv2012

A new family of implicit fourth order compact schemes for unsteady convection-diffusion equation with variable convection coefficient

In this paper, a new family of implicit compact finite difference schemes for computation of unsteady convection-diffusion equation with variable convection coefficient is proposed. The schemes are fourth order accurate in space and second or lower order accurate in time depending on the choice of weighted time average parameter. The proposed schemes, where transport variable and its first derivatives are carried as the unknowns, combine virtues of compact discretization and Pad\'{e} scheme for spatial derivative. These schemes which are based on five point stencil with constant coefficients, named as \emph{(5,5) Constant Coefficient 4th Order Compact} [(5,5)CC-4OC], give rise to a diagonally dominant system of equations and shows higher accuracy and better phase and amplitude error characteristics than some of the standard methods. These schemes are capable of using a grid aspect ratio other than unity and are unconditionally stable. They efficiently capture both transient and steady solutions of linear and nonlinear convection-diffusion equations with Dirichlet as well as Neumann boundary condition. The proposed schemes can be easily implemented and are applied to problems governed by incompressible Navier-Stokes equations apart from linear convection-diffusion equation. Results obtained are in excellent agreement with analytical and available numerical results in all cases, establishing efficiency and accuracy of the proposed scheme.

math-ph↗