Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 9 of 9 for “"summation by parts"”.
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Stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition
… problems. The overlap is treated by splitting the domain into pieces and using newly derived generalized summation-by-parts derivative operators and polynomial interpolation. Numerical regularization is not required for stability in the linear limit. Applications to linear and …
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Stable and high order accurate finite difference method for the incompressible laminar boundary layer equations
… estimate. The semidiscrete problem is formulated by discretizing the continuous spatial derivatives using high order finite difference approximations on summation-by-parts form. The boundary conditions are implemented weakly using the simultaneous approximation terms methods. The discrete energy …
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Discrete Fractional Calculus and Its Applications to Tumor Growth
… it is also possible to extend this theory by means of discrete fractional calculus and make <i>n</i>- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional …
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Towards a hybrid CFD platform for investigating aircraft trailing vortices
… achieved in a stable manner through the use of Summation-by-Parts operators and weak imposition of boundary conditions through Simultaneous-Approximation-Terms (SBP-SAT). Accordingly, a special parallel SBP-SAT interface library is developed in Elemental®. In addition, the code is extended to …
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Time-stable high-order finite difference methods for overset grids
… treatments for overset grids are stabilized by adding numerical dissipation without any underlying theoretical analysis, impacting the accuracy and the conservation properties of the original method. In this work we discuss the construction of a provably time-stable and conservative method …
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A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations
… using high-order finite difference methods on summation-by-parts form and implement the boundary conditions weakly using the simultaneous approximation term method. By applying the discrete energy method and imitating the continuous analysis, the discrete estimate that resembles the con- …
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Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory
… is ``not too far'' from the series of fractional parts $$ \sum_{n=1}^{\infty}\frac{a \{a^{-1} (n+1)\}-b\{b^{-1}(n+1)\}}{n(n+1)} \text{,}$$ i.e, the absolute value of the difference of these two quantities is less than one plus a ``small'' constant $k(a,b)$. In order to prove this result, we first …
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High-Order Positivity-Preserving <i>L<sub>2</sub></i>-Stable Spectral Collocation Schemes for the 3-D Compressible Navier-Stokes Equations
… viscous flows. The new schemes are constructed by combining a positivity-violating entropy stable method of arbitrary order of accuracy and a novel first-order positivity-preserving entropy stable method discretized on the same Legendre-Gauss-Lobatto (LGL) collocation points used for the …
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An exact and consistent adjoint method for high-fidelity discretization of the compressible flow equations
… utility of such predictions since they do not, by themselves, indicate a route to design improvement. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs. Such methods have enabled sensitivity analysis and active control of turbulence at engineering …