Scalar conservation and boundedness in simulations of compressible flow

Mixing, scalar boundedness, and numerical dissipation in large-eddy simulations

“…If the SGS model does not provide adequate dissipation for a sufficiently smooth scalar field, dispersive oscillations can produce unphysical scalar excursions [17]. These excursions are commonly mitigated using upwind schemes [18,19], or bound-preserving limiters [20,21], both of which introduce artificial dissipation and can lower the accuracy of numerical solutions.…”

“…From among the desirable properties of high-order accuracy, conservation, and boundedness, numerical schemes generally satisfy the former two properties but do not strictly impose the third. To enforce scalar boundedness, commonly-used approaches compromise either accuracy, for example with bound-preserving low-order schemes [18,19,21], or conservation, with semi-Lagrangian schemes employing bounded interpolation [20]. In this work, limiting approaches for incompressible-flow simulations that ensure scalar boundedness and conservation while preserving uniform high-order accuracy are discussed.…”

“…Liu & Osher [22] developed a linear-scaling limiter for scalar-conservation laws that was adapted to ensure boundedness with uniform high-order accuracy by Zhang & Shu [23] for finite-volume and discontinuous-Galerkin discretizations. The limiter was used in combination with a first-order scheme by Subbareddy et al [21] to mitigate scalar excursions in compressible-flow simulations with finite-volume schemes. For incompressible-flow computations, a velocity reconstruction consistent with the incompressibility condition ensures boundedness without the need of incorporating a low-order scheme, thus ensuring uniform high-order accuracy.…”