| 1. |
- Abbas, Qaisar, et al.
(författare)
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A weak boundary procedure for high order finite difference approximations of hyperbolic problems
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We introduce a new weak boundary procedures for high order finite difference operators on summation-by-parts type applied to hyperbolic problems. The boundary procedure is applied in an extended domain where data is known. We show how to raise the order of accuracy for a diagonal norm based approximation and how to modify the spectrum of the resulting operator to get a faster convergence to steady-state. Furthermore, we also show how to construct better non-reflecting properties at the boundaries using the above procedure. Numerical results that corroborate the analysis are presented.
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| 2. |
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| 3. |
- Abbas, Qaisar, et al.
(författare)
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Energy Stability of the MUSCL Scheme
- 2010
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Ingår i: Proc. 7th South African Conference on Computational and Applied Mechanics. - Berlin : South African Association for Theoretical and Applied Mechanics. ; , s. 65:1-8, s. 61-68
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 4. |
- Abbas, Qaisar, 1975-
(författare)
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Weak Boundary and Interface Procedures for Wave and Flow Problems
- 2011
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, we have analyzed the accuracy and stability aspects of weak boundary and interface conditions (WBCs) for high order finite difference methods on Summations-By-Parts (SBP) form. The numerical technique has been applied to wave propagation and flow problems.The advantage of WBCs over strong boundary conditions is that stability of the numerical scheme can be proven. The boundary procedures in the advection-diffusion equation for a boundary layer problem is analyzed. By performing Navier-Stokes calculations, it is shown that most of the conclusions from the model problem carries over to the fully nonlinear case.The work was complemented to include the new idea of using WBCs on multiple grid points in a region, where the data is known, instead of at a single point. It was shown that we can achieve high accuracy, an increased rate of convergence to steady-state and non-reflecting boundary conditions by using this approach.Using the SBP technique and WBCs, we have worked out how to construct conservative and energy stable hybrid schemes for shocks using two different approaches. In the first method, we combine a high order finite difference scheme with a second order MUSCL scheme. In the second method, a procedure to locally change the order of accuracy of the finite difference schemes is developed. The main purpose is to obtain a higher order accurate scheme in smooth regions and a low order non-oscillatory scheme in the vicinity of shocks.Furthermore, we have analyzed the energy stability of the MUSCL scheme, by reformulating the scheme in the framework of SBP and artificial dissipation operators. It was found that many of the standard slope limiters in the MUSCL scheme do not lead to a negative semi-definite dissipation matrix, as required to get pointwise stability.Finally, high order simulations of shock diffracting over a convex wall with two facets were performed. The numerical study is done for a range of Reynolds numbers. By monitoring the velocities at the solid wall, it was shown that the computations were resolved in the boundary layer. Schlieren images from the computational results were obtained which displayed new interesting flow features.
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| 7. |
- Eriksson, Sofia, et al.
(författare)
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A stable and conservative method for locally adapting the design order of finite difference schemes
- 2011
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Ingår i: Journal of Computational Physics. - : Elsevier BV. - 0021-9991 .- 1090-2716. ; 230:11, s. 4216-4231
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Tidskriftsartikel (refereegranskat)abstract
- A procedure to locally change the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be accurate and stable. Numerical experiments verify the theoretical accuracy for smooth solutions. In addition, shock calculations are performed, using a scheme where the developed switching procedure is combined with the MUSCL technique.
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| 8. |
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| 9. |
- Eriksson, Sofia, et al.
(författare)
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A stable and conservative method of locally adapting the design order of finite difference schemes
- 2010
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Ingår i: Proceedings of the 7th South African Conference on Computational and Applied Mechanics. - : South African Association for Theoretical and Applied Mechanics. - 9781634397148 ; , s. 128-136
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- A procedure to switch the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be stable and accurate.Numerical experiments verify the theoretical accuracy for smooth solutions. In addition shock calculations is performed, using a scheme where the developed switching procedure is combined with the MUSCL technique for shock capturing.
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| 10. |
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