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High-resolution half-step compact numerical approximation for 2D quasilinear elliptic equations in vector form and the estimates of normal derivatives on an irrational domain

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Abstract

This paper describes a novel implicit fourth-order approximation for solving the 2D quasilinear elliptic partial differential equations on an irrational domain. In this technique, we use 9-grid points compact cell with half-step unequal mesh discretization in both x- and y-coordinates. We also study fourth-order explicit approximations for the solution of normal derivatives on an irrational domain. The proposed method has been extended to solve quasilinear elliptic equations in vector form. Stability analysis is discussed in order to verify the convergence of the proposed computational method. On applications, we solve several benchmark nonlinear elliptic problems including steady-state Burgers’ and Navier–Stokes equations. The outcome of numerical results is shown the reliability, accuracy and the stability character of the method even for high values of Re.

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Authors and Affiliations

  1. Department of Electrical and Computer Science, University of Delaware, Newark, DE, 19716, USA

    Ishaani Priyadarshini

  2. Department of Applied Mathematics, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi, 110021, India

    R. K. Mohanty

Authors
  1. Ishaani Priyadarshini
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  2. R. K. Mohanty
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Correspondence to R. K. Mohanty.

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Priyadarshini, I., Mohanty, R.K. High-resolution half-step compact numerical approximation for 2D quasilinear elliptic equations in vector form and the estimates of normal derivatives on an irrational domain. Soft Comput 25, 9967–9991 (2021). https://doi.org/10.1007/s00500-020-05505-3

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