Investigation of supersonic underexpanded jets using adaptive unstructured finite elements

Weakly and strongly underexpanded, axisymmetric, supersonic jets are studied using unstructured, triangular finite elements. A point-implicit method with an approximate Riemann solver is utilized. These jets pose computational difficulties due to the considerable velocity gradients within their shear layers as well as the rich wave structure of their cores. A fully automatic triangular-mesh generator is implemented with the capability to adapt to the local scales of the flow and stretch in the direction normal to the local gradients. An error indicator, based on a combination of the true error estimate with the solution gradients is used. This indicator provides excellent resolution of discontinuities on modestly-refined grids. An eigenvalue filtering procedure is incorporated to allow for a more equitable distribution of the fine-mesh spacing. Mildly and strongly underexpanded jets are studied using the compressible Euler equations. The simulation results are compared with physics, as well as solutions other simulation methods. Some caveats regarding the validity of the solutions are raised.