4 papers
Direct numerical simulations of the supersonic Taylor--Green vortex via the Boltzmann equation
Tarik Dzanic, Will Trojak, Luigi Martinelli
We explore the dynamics of the three-dimensional compressible Taylor--Green vortex from the perspective of kinetic theory by directly solving the six-dimensional Boltzmann equation…
Second-order invariant-domain preserving approximation to the multi-species Euler equations
Bennett Clayton, Tarik Dzanic, Eric J. Tovar
This work is concerned with constructing a second-order, invariant-domain preserving approximation of the compressible multi-species Euler equations where each species is modeled b…
A method for bounding high-order finite element functions: Applications to mesh validity and bounds-preserving limiters
Tarik Dzanic, Tzanio Kolev, Ketan Mittal
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear boundi…
High-order limiting methods using maximum principle bounds derived from the Boltzmann equation I: Euler equations
Tarik Dzanic, Luigi Martinelli
The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In thi…