GP-MOOD: A positivity-preserving high-order finite volume method for hyperbolic conservation laws

KFVM-WENO: A High-order Accurate Kernel-based Finite Volume Method for Compressible Hydrodynamics

“…As seen in Figures 11 and 12, the overall evolution of the jets, the flow dynamics surrounding the jet envelopes, and the internal flow structures such as Kelvin-Helmholtz instabilities in the "cocoon" region are all well captured and show excellent agreement with the results studied in Ha & Gardner (2008), Balsara (2012), Bourgeois & Lee (2022). Our results assure that the present scheme is capable of simulating highly compressible flows where the shock strengths are much beyond the typical supersonic, hypersonic, and high-hypersonic regimes.…”

“…The described WENO procedure is effective but considerably more expensive than directly forming an unlimited highaccuracy reconstruction using the whole stencil. Additionally, there are relatively few cells where the nonlinear limited WENO reconstruction is truly needed (Clain et al 2011;Bourgeois & Lee 2022). Hence, if a relatively cheap indicator can flag the cells that actually need WENO, then the cheaper unlimited reconstruction can be used elsewhere.…”

“…The initial conditions must be set accurately if the succeeding evolution is to be meaningful (see, e.g., Bourgeois & Lee 2022). Here the initial cell averages are filled using a tensor-product Gauss-Legendre rule on each cell.…”

“…Here, we consider the high-density and low-density astrophysical jet problems from Balsara (2012), Bourgeois &Lee (2022), andHa &Gardner (2008), as well as an extension of the low-density jet to three dimensions. The domain used is Ω = [0, 0.5] × [0, 1.5] in two dimensions and Ω = [0, 0.5] × [0, 1.5] × [0, 0.5] in three dimensions.…”

“…The simplicity of achieving accuracy in higher spatial dimensions is mainly due to the fact that FDMs evolve pointwise quantities. In comparison, FVMs evolve volume-averaged (or cell-averaged) quantities, which complicates the design of reconstruction schemes in multiple spatial dimensions at higher than second order (Balsara 2009;Balsara et al 2009;McCorquodale & Colella 2011;Zhang et al 2011;Bourgeois & Lee 2022).…”