An asymptotically stable compact upwind-biased finite-difference scheme for hyperbolic systems

Jocksch, A.; Adams, Nikolaus A.; Kleiser, Leonhard

doi:10.1016/j.jcp.2005.01.030

Cited by 4 publications

(3 citation statements)

References 20 publications

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“…It is obvious that both A and P in eqns. (14)(15)(16)(17) are invertible matrices. Assuming that (24) where S is a diagonal matrix, and its diagonal line is constituted by the eigenvalues of Q, then substituting eqn.…”

Section: Stability Analysis Of Hamr Complete Schemementioning

confidence: 99%

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Optimized Compact Finite Difference Schemes with High Accuracy and Maximum Resolution

Liu

Huang

Zhao

et al. 2008

International Journal of Aeroacoustics

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The pentadiagonal compact finite difference scheme and asymmetric boundary schemes are optimized with high accuracy and maximum resolution in this paper. Through Fourier analysis, the optimization is reduced to the problem of finding the minimum of a multivariable nonlinear function with multiple constraints. The advanced sequential quadratic programming method is employed to find the minimum. In order to extend the resolution characteristic of the schemes, the wavenumber domain for optimization is nearly identical to the well-resolved domain, and the maximum well-resolved wavenumber is obtained by means of equal step length searching. The optimized schemes are strictly stable as confirmed by an eigenvalue analysis. The increased performances of the schemes are demonstrated through their application to one-and twodimensional examples and are compared with other schemes optimized before.

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Section: Stability Analysis Of Hamr Complete Schemementioning

confidence: 99%

“…In recent years, many optimized or reformulated compact finite difference schemes have been proposed [10][11][12][13][14][15][16][17][18]. Lele [10] reformulated the well-known Padé schemes and improved their resolution.…”

Section: Introductionmentioning

confidence: 99%

Optimized Compact Finite Difference Schemes with High Accuracy and Maximum Resolution

Liu

Huang

Zhao

et al. 2008

International Journal of Aeroacoustics

View full text Add to dashboard Cite

show abstract

“…Shen et al [20] demonstrated a new way of constructing high accuracy shock-capturing compact schemes. Jocksch et al [21] developed a fifth order compact upwind-biased finite difference scheme for compressible Couette flow. Mohamad et al [22] presented a third order compact upwind scheme for flows containing discontinuities.…”

Section: Introductionmentioning

confidence: 99%

A Sixth Order Accuracy Solution to a System of Nonlinear Differential Equations with Coupled Compact Method

Liu

Chen

Wang

2013

Journal of Computational Engineering

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A system of coupled nonlinear partial differential equations with convective and dispersive terms was modified from Boussinesq-type equations. Through a special formulation, a system of nonlinear partial differential equations was solved alternately and explicitly in time without linearizing the nonlinearity. Coupled compact schemes of sixth order accuracy in space were developed to obtain numerical solutions. Within couple compact schemes, variables and their first and second derivatives were solved altogether. The sixth order accuracy in space is achieved with a memory-saving arrangement of state variables so that the linear system is banded instead of blocked. This facilitates solving very large systems. The efficiency, simplicity, and accuracy make this coupled compact method viable as variational and weighted residual methods. Results were compared with exact solutions which were obtained via devised forcing terms. Error analyses were carried out, and the sixth order convergence in space and second order convergence in time were demonstrated. Long time integration was also studied to show stability and error convergence rates.

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HWENO Schemes Based on Compact Differencefor Hyperbolic Conservation Laws

2018

J Sci Comput

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An asymptotically stable compact upwind-biased finite-difference scheme for hyperbolic systems

Cited by 4 publications

References 20 publications

Optimized Compact Finite Difference Schemes with High Accuracy and Maximum Resolution

Optimized Compact Finite Difference Schemes with High Accuracy and Maximum Resolution

A Sixth Order Accuracy Solution to a System of Nonlinear Differential Equations with Coupled Compact Method

HWENO Schemes Based on Compact Differencefor Hyperbolic Conservation Laws

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