Nonlinear waves propagation and stability analysis for planar waves at far field using quintic B-spline collocation method

Abstract

A study of the dynamics of nonlinear waves at far field has been presented for real gases using quintic B-spline collocation method. To examine the dynamics at far field, “fast variable” in the governing system of equations has been introduced. Using asymptotic expansion of the flow variables in new fast variables, an evolution equation has been obtained for the behavior of waves at far from source. The evolution equation is modified Burger’s equation, which is known to have exact solution for planar flow. However, the solution for the corresponding cylindrical and spherical symmetric flow for the equation is unknown. The obtained numerical results have been compared with the exact solution for the planar flow. The error norms of numerically computed values are found very small when compared to corresponding exact solution. A Von Neumann stability analysis of the scheme is presented. The scheme is found unconditionally stable. It shows that the method is quite efficient to capture the dynamics of flow at far field. Results corresponding to other two geometries have been presented at different time. Further, a study on the effect of the real medium on the flow is presented. Schematic shows that with the increase in non-ideal property of the medium, the formation of shock becomes faster.

Keywords

• Far-field
• Symmetric flow
• Conservation laws
• Quintic B-spline
• Collocation method