On the implementation of a multi–property-preserving strategy for a high-order modal discontinuous Galerkin solver

In this work, we propose a multi-property-preserving modal DG framework for compressible flows enforcing both entropy balance and a physically admissible kinetic energy evolution. The approach is formulated within the Direct Enforcement of Entropy Balance (DEEB) framework. The explicit residual correction for entropy is extended to account for the additional discretization errors that emerge in the embedded kinetic energy equation. A key advantage of the proposed in-cell strategy is its limited computational cost relative to the baseline scheme, particularly when compared with alternative strategies based on two-point volume flux-differencing techniques. The framework is extensively validated against inviscid benchmarks and scale-resolving simulations, showing that the proposed method retains optimal accuracy on smooth flows, exhibits extreme robustness in shock-driven tests, and provides high fidelity in capturing turbulent statistics on highly under-resolved grids.