Calculation of Four-Dimensional Unsteady Gas Flow via Different Quadrature Schemes and Runge-Kutta 4th Order Method (Advances in Applied Mathematics and Mechanics, 2024)
In this study, a (3+1) dimensional unstable gas flow system is appliedand solved successfully via differential quadrature techniques based on variousshape functions. The governing system of nonlinear four-dimensional unsteadyNavier–Stokes equations of gas dynamics is reduced to the system of nonlinear ordinary differential equations using different quadrature techniques. Then, Runge-Kutta4th order method is employed to solve the resulting system of equations. To obtainthe solution of this equation, a MATLAB code is designed. The validity of these techniques is achieved by the comparison with the exact solution where the error reachto $≤ 1×10^{−5}.$ Also, these solutions are discussed by seven various statistical analysis. Then, a parametric analysis is presented to discuss the effect of adiabatic indexparameter on the velocity, pressure, and density profiles. From these computations, itis found that Discrete singular convolution based on Regularized Shannon kernels is astable, efficient numerical technique and its strength has been appeared in this application. Also, this technique can be able to solve higher dimensional nonlinear problemsin various regions of physical and numerical sciences.