Explicit and Implicit Kinetic Streamlined-Upwind Petrov Galerkin Method for Hyperbolic Partial Differential Equations
This work presents an incremental improvement to stabilized finite element methods for solving hyperbolic PDEs, targeting computational scientists and engineers.
The paper introduces a novel explicit and implicit Kinetic Streamlined-Upwind Petrov Galerkin (KSUPG) scheme for hyperbolic equations, demonstrating better performance than the original SUPG method in multi-dimensions through numerical experiments on Burgers and Euler equations.
A novel explicit and implicit Kinetic Streamlined-Upwind Petrov Galerkin (KSUPG) scheme is presented for hyperbolic equations such as Burgers equation and compressible Euler equations. The proposed scheme performs better than the original SUPG stabilized method in multi-dimensions. To demonstrate the numerical accuracy of the scheme, various numerical experiments have been carried out for 1D and 2D Burgers equation as well as for 1D and 2D Euler equations using Q4 and T3 elements. Furthermore, spectral stability analysis is done for the explicit 2D formulation. Finally, a comparison is made between explicit and implicit versions of the KSUPG scheme.