The compressible Euler equations interface includes a weighted essentially nonoscillatory (WENO) limiter for use in the discontinuous Galerkin method, which is applied in each inner stage of the time-explicit solver. The WENO limiter reconstructs the polynomial of the DG solution in a troubled element from a convex combination of the polynomials in the current element and its immediate neighbors based on smoothness indicators and nonlinear weights, and includes adjustments to guarantee conservation. A total variation bounded (TVB) troubled cell indicator is available to limit the use of WENO to the elements where it is needed and reduce computational costs. The TVB constant can be set by the user and a larger value means that a smaller number of elements will use WENO. For more information on the WENO limiter, see Ref. 2.

The compressible Euler equations are well posed only if both density and pressure are positive. When using constant interpolations, the positivity of density and pressure is guaranteed if the CFL condition for the time step is satisfied. If the dependent variables are discretized with linear shape functions, the positivity of density and pressure is not ensured even when satisfying the CFL condition and using the WENO limiter. Therefore, the physics interface includes a positivity-preserving limiter for density and pressure which can be used together with WENO to prevent numerical blow-ups. See Ref. 3 for more information.