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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2605.08105 |
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| _version_ | 1866910202409779200 |
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| author | Chamarthi, Amareshwara Sainadh |
| author_facet | Chamarthi, Amareshwara Sainadh |
| contents | In wall-modelled large-eddy simulations of hypersonic boundary-layer transition, Hoffmann, Chamarthi and Frankel reported that characteristic reconstruction based on conservative-variable eigenvectors produced markedly better results than the corresponding primitive-variable implementation. The observation was empirical. A subsequent wave-appropriate conservative reconstruction (WA-CR) algorithm used a rank-one entropy correction based on the premise that contact-discontinuity error lies in a single conservative entropy/contact direction. This note gives the algebraic foundation for both observations. For the standard conservative curvilinear eigenvectors, the density row of the right-eigenvector matrix contains exact, metric-free zeros in the shear columns, so shear waves carry no density perturbation and a contact discontinuity is represented by the conservative entropy eigenvector alone. The conservative left eigenvectors provide the dual projection property: the entropy amplitude is obtained with a metric-independent left eigenvector and has unit contact scaling, while total-energy perturbations have zero projection onto the shear amplitudes. In the standard primitive curvilinear eigenvectors, by contrast, shear right eigenvectors contain metric-dependent density components and the primitive entropy left eigenvector contains metric-weighted tangential-velocity terms. Thus the conservative formulation supplies the two algebraic requirements for an exact, sufficient, metric-invariant, rank-one entropy correction: metric-independent entropy projection and a metric-independent entropy update direction. Curvilinear metrics make the distinction explicit, but the conservative state-space contact direction is already the natural direction underlying WA-CR even on Cartesian grids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08105 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Reconstructing Conservative and Primitive Variables: An Eigenvector Analysis on Curvilinear Grids Chamarthi, Amareshwara Sainadh Computational Physics In wall-modelled large-eddy simulations of hypersonic boundary-layer transition, Hoffmann, Chamarthi and Frankel reported that characteristic reconstruction based on conservative-variable eigenvectors produced markedly better results than the corresponding primitive-variable implementation. The observation was empirical. A subsequent wave-appropriate conservative reconstruction (WA-CR) algorithm used a rank-one entropy correction based on the premise that contact-discontinuity error lies in a single conservative entropy/contact direction. This note gives the algebraic foundation for both observations. For the standard conservative curvilinear eigenvectors, the density row of the right-eigenvector matrix contains exact, metric-free zeros in the shear columns, so shear waves carry no density perturbation and a contact discontinuity is represented by the conservative entropy eigenvector alone. The conservative left eigenvectors provide the dual projection property: the entropy amplitude is obtained with a metric-independent left eigenvector and has unit contact scaling, while total-energy perturbations have zero projection onto the shear amplitudes. In the standard primitive curvilinear eigenvectors, by contrast, shear right eigenvectors contain metric-dependent density components and the primitive entropy left eigenvector contains metric-weighted tangential-velocity terms. Thus the conservative formulation supplies the two algebraic requirements for an exact, sufficient, metric-invariant, rank-one entropy correction: metric-independent entropy projection and a metric-independent entropy update direction. Curvilinear metrics make the distinction explicit, but the conservative state-space contact direction is already the natural direction underlying WA-CR even on Cartesian grids. |
| title | On Reconstructing Conservative and Primitive Variables: An Eigenvector Analysis on Curvilinear Grids |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2605.08105 |