Abstract
In this work, we propose a new upwind compact scheme with appropriately designed new boundary closures. The scheme is obtained by minimizing weighted dispersion error and is asymptotically stable. As the formulation leads to an implicit tridiagonal system for approximating spatial derivative it is computationally efficient for long time simulation. The scheme thus derived is tested in conjunction with explicit and implicit time advancing strategies. Verification and validation studies help establish the newly developed method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Lele, S.K.: Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42 (1992)
Vishal, M.R., Gaitonde, D.V.: On the use of higher-order finite-difference schemes on curvilinear and deforming meshes. J. Comput. Phys. 181, 155–185 (2002)
Zhong, X.: High-order finite-difference schemes for numerical simulation of hypersonic boundary-layer transition. J. Comput. Phys. 144, 662–709 (1998)
Sengupta, T.K., Ganeriwal, G., De, S.: Analysis of central and upwind compact schemes. J. Comput. Phys. 192, 677–694 (2003)
Rai, M.M., Moin, P.: Direct numerical simulation of transition and turbulence in a spatially evolving boundary layer. J. Comput. Phys. 109, 169–192 (1993)
Bhumkar, Y.G., Sheu, T.W.H., Sengupta, T.K.: A dispersion relation preserving optimized upwind compact difference scheme for high accuracy flow simulations. J. Comput. Phys. 278, 378–399 (2014)
Tam, C.K.W., Webb, J.C.: Dispersion-relation-preserving finite difference schemes for computational acoustics. J. Comput. Phys. 107, 262–281 (1993)
Gustafsson, B., Kreiss, H.-O., Sundström, A.: Stability theory of difference approximation for mixed initial boundary value problems II. Math. Comput. 26, 649–686 (1972)
Carpenter, M.H., Gottlieb, D., Abarbanel, S.: Stable and accurate boundary treatments for compact high-order finite-difference schemes. Appl. Numer. Math. 12, 55–87 (1993)
Carpenter, M.H., Gottlieb, D., Abarbanel, S.: The stability of numerical boundary treatments for compact high-order finite-difference schemes. J. Comput. Phys. 108, 272–295 (1993)
Haras, Z., Ta’asan, S.: Finite difference schemes for long time integration. J. Comput. Phys. 114, 265–279 (1994)
Giri, S., Sen, S.: A new class of diagonally implicit Runge-Kutta methods with zero dissipation and minimized dispersion error. J. Comput. Appl. Math. 376, 112841 (2020)
Butcher, J.: Numerical Methods for Ordinary Differential Equations. Wiley, West Sussex (2008)
Sen, S.: A new family of (5,5) CC-4OC schemes applicable for unsteady Navier-Stokes equations. J. Comput. Phys. 251, 251–271 (2013)
Acknowledgement
The second author is thankful to Science & Engineering Research Board, India for assistance under Mathematical Research Impact Centric Support (File Number: MTR/2017/000038).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Giri, S., Sen, S. (2021). A New (3, 3) Low Dispersion Upwind Compact Scheme. In: Awasthi, A., John, S.J., Panda, S. (eds) Computational Sciences - Modelling, Computing and Soft Computing. CSMCS 2020. Communications in Computer and Information Science, vol 1345. Springer, Singapore. https://doi.org/10.1007/978-981-16-4772-7_10
Download citation
DOI: https://doi.org/10.1007/978-981-16-4772-7_10
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-4771-0
Online ISBN: 978-981-16-4772-7
eBook Packages: Computer ScienceComputer Science (R0)