Higher-Order Gauss–Lobatto Integration for Non-Linear Hyperbolic Equations

Maerschalck, B. De; Gerritsma, Marc

doi:10.1007/s10915-005-9052-x

Cited by 19 publications

(11 citation statements)

References 23 publications

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“…An integration order P = 8 is chosen, see (23). De Maerschalck and Gerritsma [37] demonstrated that over-integration is beneficial for non-smooth problems to account for the slowly decaying higher-order modes in the system. At the outflow boundary, the exit pressure is set at p = 1.…”

Section: Results For Subsonic Flowmentioning

confidence: 99%

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Least‐squares spectral element method applied to the Euler equations

Gerritsma

Bas

Maerschalck

et al. 2008

Numerical Methods in Fluids

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SUMMARYThis paper describes the application of the least-squares spectral element method to compressible flow problems. Special attention is paid to the imposition of the weak boundary conditions along curved walls and the influence of the time step on the position and resolution of shocks. The method is described and results are presented for a supersonic flow over a wedge and subsonic, transonic and supersonic flow problems over a bump.

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Section: Results For Subsonic Flowmentioning

confidence: 99%

“…It has been shown in [37] that it is beneficial for non-linear equations possessing large gradients to choose the integration order P higher than the approximation of the solution, N .…”

Section: Spectral Elementsmentioning

confidence: 99%

Least‐squares spectral element method applied to the Euler equations

Gerritsma

Bas

Maerschalck

et al. 2008

Numerical Methods in Fluids

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“…Thus, it is possible to determine a priori for a given problem the optimal order of Q. Depending on the characteristics of the solution and of the non-constant coefficients, overintegration can improve the convergence rate of the solution [39,40].…”

Section: The Fully Discrete Modelmentioning

confidence: 99%

The least squares spectral element method for the Cahn–Hilliard equation

Fernandino

Dorao

2011

Applied Mathematical Modelling

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a b s t r a c tThe problem of numerically resolving an interface separating two different components is a common problem in several scientific and engineering applications. One alternative is to use phase field or diffuse interface methods such as the Cahn-Hilliard (C-H) equation, which introduce a continuous transition region between the two bulk phases. Different numerical schemes to solve the C-H equation have been suggested in the literature. In this work, the least squares spectral element method (LS-SEM) is used to solve the CahnHilliard equation. The LS-SEM is combined with a time-space coupled formulation and a high order continuity approximation by employing C 11 p-version hierarchical interpolation functions both in space and time. A one-dimensional case of the Cahn-Hilliard equation is solved and the convergence properties of the presented method analyzed. The obtained solution is in accordance with previous results from the literature and the basic properties of the C-H equation (i.e. mass conservation and energy dissipation) are maintained. By using the LS-SEM, a symmetric positive definite problem is always obtained, making it possible to use highly efficient solvers for this kind of problems. The use of dynamic adjustment of number of elements and order of approximation gives the possibility of a dynamic meshing procedure for a better resolution in the areas close to interfaces.

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“…Depending on the characteristic of the solution and of the non-constant coefficients, overintegration, i.e. P > N, can improve the convergence rate of the solution [16,18]. A final remark is that the integral terms in the operator (3) produces a global dependency of the solution in the property dimension.…”

Section: Spectral Element Approximationmentioning

confidence: 99%