Optimization-based synchronized flux-corrected conservative interpolation (remapping) of mass and momentum for arbitrary Lagrangian–Eulerian methods

Formulation, analysis and numerical study of an optimization-based conservative interpolation (remap) of scalar fields for arbitrary Lagrangian–Eulerian methods

“…Under some weak requirements on grid proximity, but not on the cell types, we prove that the OBR algorithm is linearity preserving in one, two and three dimensions. The paper also examines connections between the OBR and the recently proposed flux-corrected remap (FCR), Liska et al [1]. We show that the FCR solution coincides with the solution of a modified version of OBR (M-OBR), which has the same objective but a simpler set of box constraints derived by using a ''worst-case'' scenario.…”

Synchronized flux corrected remapping for ALE methods

“…The minimum is always in one of the polygon's vertices, the polygon is intersection of eight half-planes (given by linear constraints), so the minimization in this case is easy. For more details on synchronized FCR for density and momentum see [13], where the choice of dimensional factors in a global deviation (the global analog of (6)) is made to produce a local minimization problem which is computationally efficient. Sensitivity to the choice of dimensional factors has not been investigated.…”

“…Compared to the sequential FCR [12], we apply the bounds simultaneously to treat all quantities in the system at once, thus we call our method synchronized FCR (SFCR). The SFCR method has been developed in [13] for mass and momentum with bounds in density and velocity. Here we extend it to include also remap of total energy with bounds in internal energy.…”

“…For the description of S&S remapping and Table 1 Convergence tables (L 1 errors and their ratios) in density, velocity and internal energy for cyclic remapping of simple shock by low-order, high-order, SFCR and S&S methods. its comparison with SFCR see [13]. The SFCR method produces smaller errors than both high-order and S&S methods.…”

Sequential limiting in continuous and discontinuous Galerkin methods for the Euler equations

“…Synchronized limiters [12,14,15,19,21] use the same correction factor for all components or a set of balanced correction factors for different components. The latter approach typically leads to constrained optimization problems [16] rather than closed-form expressions.…”