Numerical methods for the calculation of three-dimensional nozzle exhaust flow fields

Numerical codes developed for the calculation of three-dimensional nozzle exhaust flow fields associated with hypersonic airbreathing aircraft are described. Both codes employ reference plane grid networks with respect to three coordinate systems. Program CHAR3D is a characteristic code utilizing a new wave preserving network within the reference planes, while program BIGMAC is a finite difference code utilizing conservation variables and a one-sided difference algorithm. Secondary waves are numerically captured by both codes, while the underexpansion shock and plume boundary are treated discretely. The exhaust gas properties consist of hydrogen-air combustion product mixtures in local chemical equilibrium. Nozzle contours are treated by a newly developed geometry package based on dual cubic splines. Results are presented for simple configurations demonstrating two- and three-dimensional multiple wave interactions

High-order interpolation between adjacent cartesian finite difference grids of different size

Nested cartesian grid systems by design require interpolation of solution fields from coarser to finer grid systems. While several choices are available, preserving accuracy, stability and efficiency at the same time require careful design of the interpolation schemes. Given this context, a series of interpolation algorithms for nested cartesian finite difference grids of different size were developed and tested. These algorithms are based on post-processing, on each local grid, the raw (bi/trilinear) information passed to the halo points from coarser grids. In this way modularity is maximized while preserving locality. The results obtained indicate that the schemes improve markedly the convergence rates and the overall accuracy of finite difference codes with varying grid sizes.Publicado en: Mecánica Computacional vol. XXXV, no. 15Facultad de Ingenierí

High-order interpolation between adjacent cartesian finite difference grids of different size

Nested cartesian grid systems by design require interpolation of solution fields from coarser to finer grid systems. While several choices are available, preserving accuracy, stability and efficiency at the same time require careful design of the interpolation schemes. Given this context, a series of interpolation algorithms for nested cartesian finite difference grids of different size were developed and tested. These algorithms are based on post-processing, on each local grid, the raw (bi/trilinear) information passed to the halo points from coarser grids. In this way modularity is maximized while preserving locality. The results obtained indicate that the schemes improve markedly the convergence rates and the overall accuracy of finite difference codes with varying grid sizes.Publicado en: Mecánica Computacional vol. XXXV, no. 15Facultad de Ingenierí

High-order interpolation between adjacent cartesian finite difference grids of different size

Nested cartesian grid systems by design require interpolation of solution fields from coarser to finer grid systems. While several choices are available, preserving accuracy, stability and efficiency at the same time require careful design of the interpolation schemes. Given this context, a series of interpolation algorithms for nested cartesian finite difference grids of different size were developed and tested. These algorithms are based on post-processing, on each local grid, the raw (bi/trilinear) information passed to the halo points from coarser grids. In this way modularity is maximized while preserving locality. The results obtained indicate that the schemes improve markedly the convergence rates and the overall accuracy of finite difference codes with varying grid sizes.Publicado en: Mecánica Computacional vol. XXXV, no. 15Facultad de Ingenierí

Floquetifying the Colour Code

Floquet codes are a recently discovered type of quantum error correction code. They can be thought of as generalising stabilizer codes and subsystem codes, by allowing the logical Pauli operators of the code to vary dynamically over time. In this work, we use the ZX-calculus to create new Floquet codes that are in a definable sense equivalent to known stabilizer codes. In particular, we find a Floquet code that is equivalent to the colour code, but has the advantage that all measurements required to implement it are of weight one or two. Notably, the qubits can even be laid out on a square lattice. This circumvents current difficulties with implementing the colour code fault-tolerantly, while preserving its advantages over other well-studied codes, and could furthermore allow one to benefit from extra features exclusive to Floquet codes. On a higher level, as in arXiv:2303.08829, this work shines a light on the relationship between 'static' stabilizer and subsystem codes and 'dynamic' Floquet codes; at first glance the latter seems a significant generalisation of the former, but in the case of the codes that we find here, the difference is essentially just a few basic ZX-diagram deformations.Comment: 15 + 24 pages, 18 figures. Comments encouraged - email address in paper