Similarity solutions for cylindrical shock wave in self‐gravitating non‐ideal gas with axial magnetic field: Isothermal flow

Gupta, Nandita; Sharma, Kajal; Arora, Rajan

doi:10.1002/mma.7850

Cited by 7 publications

(1 citation statement)

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“…To overcome these problems, a powerful tool is needed to alleviate this computational burden and enhance efficiency by reducing the independent variables. The similarity method is one of the most commonly used techniques for reducing independent variables and has been applied to many problems [19][20][21][22][23]. In fact, Blasius [24] originally proposed the similarity solution to solve an application problem of Prandtl's boundary layer theory.…”

Section: Introductionmentioning

confidence: 99%

A Rotated Similarity Reduction Approach with Half-Sweep Successive Over-Relaxation Iteration for Solving Two-Dimensional Unsteady Convection-Diffusion Problems

Ali¹,

Sulaiman²,

Saudi³

et al. 2023

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In this paper, we transformed a two-dimensional unsteady convection-diffusion equation into a two-dimensional steady convection-diffusion equation using the similarity transformation technique. This technique can be easily applied to linear or nonlinear problems and is capable of reducing the size of computational works since the main idea of this technique is to reduce at least one independent variable. The corresponding similarity equation is then solved numerically using an effective numerical technique, namely a new five-point rotated similarity finite difference scheme via half-sweep successive over-relaxation iteration. This work compared the performance of the proposed method with Gauss-Seidel and successive over-relaxation with the full-sweep concept. Numerical tests were carried out to obtain the performance of the proposed method using C simulation. The results revealed that the combination of the five-point rotated similarity finite difference scheme via half-sweep successive over-relaxation iteration is the most superior method in terms of the iteration number and computational time compared to all these methods. Additionally, in terms of accuracy, all three iterative methods are also comparable.

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