My Way: A Computational Autobiography

doi:10.1007/s42967-019-00021-0

Abstract

Philip Roe. My Way: A Computational Autobiography[J]. Communications on Applied Mathematics and Computation, 2020, 2(3): 321-340.

TrendMD

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: https://www.camc.shu.edu.cn/EN/10.1007/s42967-019-00021-0

https://www.camc.shu.edu.cn/EN/Y2020/V2/I3/321

1. Barsukow, W.:Stationarity preserving schemes for multi-dimensional linear systems. Mathematics of Computation (2018)
2. Berthon, C., Breu, M., Titeux, M.O.:A relaxation scheme for the approximation of the pressureless Euler equations. Numer. Methods Partial Difer. Equ. 22(2), 484-505 (2006)
3. Bouche, D., Bonnaud, G., Ramos, D.:Comparison of numerical schemes for solving the advection equation. Appl. Math. Lett. 16(2), 147-154 (2003)
4. Chima, R., Liou, M.S.:Comparison of the AUSM+ and H-CUSP schemes for turbomachinery applications. In:16th AIAA Computational Fluid Dynamics Conference, p. 4120 (2003)
5. Courant, R., Friedrichs, K.O.:Supersonic Flow and Shock Waves. Springer, Berlin (1999)
6. Deconinck, H., Paillere, H., Struijs, R., Roe, P.L.:Multidimensional upwind schemes based on fuctuation-splitting for systems of conservation laws. Comput. Mech. 11(5/6), 323-340 (1993)
7. Deconinck, H., Ricchiuto, M.:Residual distribution schemes:foundations and analysis, 2nd edn, pp. 1-53. Encyclopedia of Computational Mechanics (2018)
8. Deconinck, H., Roe, P.L., Struijs, R.:A multidimensional generalization of Roe's fux diference splitter for the Euler equations. Comput. Fluids 22(2/3), 215-222 (1993)
9. Després, B.:Uniform asymptotic stability of Strang's explicit compact schemes for linear advection. SIAM J. Numer. Anal. 47(5), 3956-3976 (2009)
10. Fan, D.:On the acoustic component of active fux schemes for nonlinear hyperbolic conservation laws. Ph.D. thesis, Department of Aerospace Engineering, University of Michigan (2017)
11. Fan, D., Roe, P.L.:Investigations of a new scheme for wave propagation. In:22nd AIAA Computational Fluid Dynamics Conference, p. 2449 (2015)
12. Fidkowski, K.J., Roe, P.L.:An entropy adjoint approach to mesh refnement. SIAM J. Sci. Comput. 32(3), 1261-1287 (2010)
13. Hall, M. G.:Cell-vertex multigrid schemes for solution of the Euler equations. In:Numerical methods for fuid dynamics, Eds Morton and Baines, pp. 303-345, Oxford University Press (1986)
14. Hedstrom, G.W.:Models of diference schemes for u_t + au_x=0 by partial diferential equations. Math. Comput. 29(132), 969-977 (1975)
15. Iserles, A.:Order stars and a saturation theorem for frst-order hyperbolics. IMA J. Numer. Anal. 2(1), 49-61 (1982)
16. Iserles, A., Strang, G.:The optimal accuracy of diference schemes. Trans. Am. Math. Soc. 277(2), 779-803 (1983)
17. Ismail, F., Roe, P.L.:Afordable, entropy-consistent Euler fux functions II:entropy production at shocks. J. Comput. Phys. 228(15), 5410-5436 (2009)
18. Jameson, A.:A vertex based multigrid algorithm for three dimensional compressible fow calculations. In:ASME Symposium on Numerical Methods for Compressible Flow, Anaheim (1986)
19. Jameson, A., Schmidt, W., Turkel, E.:Numerical solution of the Euler equations by fnite volume methods using Runge Kutta time stepping schemes. In:14th Fluid and Plasma Dynamics Conference, p. 1259 (1981)
20. Lerat, A., Falissard, F., Sides, J.:Vorticity-preserving schemes for the compressible Euler equations. J. Comput. Phys. 225(1), 635-651 (2007)
21. Lin, H.C.:Topics in numerical computation of compressible fow. Ph. D. thesis, Cranfeld Institute of Technology (1990)
22. Liu, F., Jennions, I., Jameson, A.:Computation of turbomachinery fow by a convective-upwind-splitpressure (CUSP) scheme. In:36th AIAA Aerospace Sciences Meeting and Exhibit, p. 969 (1998)
23. Lung, T.B., Roe, P.L.:Toward a reduction of mesh imprinting. Int. J. Numer. Methods Fluids 76(7), 450-470 (2014)
24. Falissard, F., Lerat, A., Sidès, J.:Computation of airfoil-vortex interaction using a vorticity-preserving scheme. AIAA J. 46(7), 1614-1623 (2008)
25. MacCormack, R.:The efect of viscosity in hypervelosity impact cratering. AIAA paper 69-354 (1969)
26. Maeng, J.B.:On the advective component of active fux schemes for nonlinear hyperbolic conservation laws. Ph.D. thesis, Department of Aerospace Engineering, University of Michigan (2017)
27. Mesaros, L., Roe, P.:Multidimensional fuctuation splitting schemes based on decomposition methods. In:12th AIAA Computational Fluid Dynamics Conference, p. 1699 (1995)
28. Mishra, S., Tadmor, E.:Constraint preserving schemes using potential-based fuxes. II. Genuinely multidimensional systems of conservation laws. SIAM Journal on Numerical Analysis, 49(3), pp.1023-1045 (2011)
29. Morton, K.W., Roe, P.L.:Vorticity-preserving Lax-Wendrof-type schemes for the system wave equation. SIAM J. Sci. Comput. 23(1), 170-192 (2001)
30. Morton, K.W., Suli, E.:Finite volume methods and their analysis. IMA J. Numer. Anal. 11(2), 241-260 (1991)
31. Morton, K.W., Paisley, M.F.:A fnite volume scheme with shock ftting for the steady Euler equations. J. Comput. Phys. 80(1), 168-203 (1989)
32. Ni, R.H.:A multiple grid scheme for solving the Euler equations. In:5th AIAA Computational Fluid Dynamics Conference, p. 1025 (1981)
33. Pettersson, P., Iaccarino, G., Nordstrm, J.:A stochastic Galerkin method for the Euler equations with Roe variable transformation. J. Comput. Phys. 257, 481-500 (2014)
34. Poisson, S.D.:Mm. Acad. Sci. Paris 3, 121-176 (1818)
35. Pulliam, T.H.:Computational challenge-Euler solution for ellipses. AIAA J. 28(10), 1703-1704 (1990)
36. Rizzi, A., Viviand, H.:Numerical methods for the computation of inviscid transonic fows with shock waves:a GAMM workshop (Vol. 3). Springer-Verlag, (available as ebook) (1981)
37. Roe, P.L.:The use of the Riemann problem in fnite diference schemes. In:Seventh International Conference on Numerical Methods in Fluid Dynamics, pp. 354-359. Springer, Berlin, Heidelberg. (1981)
38. Roe, P.L.:Approximate Riemann solvers, parameter vectors, and diference schemes. J. Comput. Phys. 43(2), 357-372 (1981)
39. Roe, P.L.:Linear advection schemes on triangular meshes. Technical Report 8720, Cranfeld College of Aeronautics, 8720 (1987)
40. Roe, P.L.:Linear bicharacteristic schemes without dissipation. SIAM J. Sci. Comput. 19, 1405-1427 (1998)
41. Roe, P.L.:Did numerical methods for hyperbolic problems take a wrong turning?. In:XVI International Conference on Hyperbolic Problems:Theory, Numerics, Applications, pp. 517-534. Springer, Cham (2016)
42. Roe, P.L., Balsara, D.S.:Notes on the eigensystem of magnetohydrodynamics. SIAM J. Appl. Math. 56(1), 57-67 (1996)
43. Roe, P.L., Maeng, J., Fan, D.:Comparing active fux and discontinuous galerkin methods for compressible fow. In:2018 AIAA Aerospace Sciences Meeting, p. 0836 (2018)
44. Roe, P.L., Sidilkover, D.:Optimum positive linear schemes for advection in two and three dimensions. SIAM J. Numer. Anal. 29(6), 1542-1568 (1992)
45. Sidikover, D.:Numerical solution to steady-state problems with discontinuities. Ph. D. thesis, The Weizmann Institute, Rahovot (1990)
46. Zhang, X., Shu, C.-W.:Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws:survey and new developments. Proc. R. Soc. A 467, 2752-2776 (2011)

[1]	Arpit Babbar, Praveen Chandrashekar. Multiderivative Runge-Kutta Flux Reconstruction for Hyperbolic Conservation Laws [J]. Communications on Applied Mathematics and Computation, 2026, 8(2): 664-704.
[2]	Dinshaw S. Balsara, Deepak Bhoriya, Chi-Wang Shu, Harish Kumar. Efficient Alternative Finite Difference WENO Schemes for Hyperbolic Conservation Laws [J]. Communications on Applied Mathematics and Computation, 2025, 7(6): 2189-2242.
[3]	Dinshaw S. Balsara, Deepak Bhoriya, Chi-Wang Shu, Harish Kumar. Efficient Alternative Finite Difference WENO Schemes for Hyperbolic Systems with Non-conservative Products [J]. Communications on Applied Mathematics and Computation, 2025, 7(6): 2289-2338.
[4]	Guangyao Zhu, Yan Jiang, Mengping Zhang. Inverse Lax-Wendroff Boundary Treatment for Solving Conservation Laws with Finite Volume Methods [J]. Communications on Applied Mathematics and Computation, 2025, 7(3): 885-909.
[5]	Lei Yang, Shun Li, Yan Jiang, Chi-Wang Shu, Mengping Zhang. Inverse Lax-Wendroff Boundary Treatment of Discontinuous Galerkin Method for 1D Conservation Laws [J]. Communications on Applied Mathematics and Computation, 2025, 7(2): 796-826.
[6]	Michael Herty, Niklas Kolbe, Siegfried Müller. A Central Scheme for Two Coupled Hyperbolic Systems [J]. Communications on Applied Mathematics and Computation, 2024, 6(4): 2093-2118.
[7]	Matania Ben-Artzi, Jiequan Li. Hyperbolic Conservation Laws, Integral Balance Laws and Regularity of Fluxes [J]. Communications on Applied Mathematics and Computation, 2024, 6(4): 2048-2063.
[8]	Feng Zheng, Jianxian Qiu. Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws [J]. Communications on Applied Mathematics and Computation, 2024, 6(1): 605-624.
[9]	John M. Holmes, Barbara Lee Keyfitz. Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws [J]. Communications on Applied Mathematics and Computation, 2024, 6(1): 489-500.
[10]	Xuan Ren, Jianhu Feng, Supei Zheng, Xiaohan Cheng, Yang Li. On High-Resolution Entropy-Consistent Flux with Slope Limiter for Hyperbolic Conservation Laws [J]. Communications on Applied Mathematics and Computation, 2023, 5(4): 1616-1643.
[11]	Matania Ben-Artzi, Jiequan Li. Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws [J]. Communications on Applied Mathematics and Computation, 2023, 5(3): 1289-1298.
[12]	R. Abgrall, J. Nordström, P. Öffner, S. Tokareva. Analysis of the SBP-SAT Stabilization for Finite Element Methods Part II: Entropy Stability [J]. Communications on Applied Mathematics and Computation, 2023, 5(2): 573-595.
[13]	Shima Baharlouei, Reza Mokhtari, Nabi Chegini. A Stable Numerical Scheme Based on the Hybridized Discontinuous Galerkin Method for the Ito-Type Coupled KdV System [J]. Communications on Applied Mathematics and Computation, 2022, 4(4): 1351-1373.
[14]	Ohannes A. Karakashian, Michael M. Wise. A Posteriori Error Estimates for Finite Element Methods for Systems of Nonlinear, Dispersive Equations [J]. Communications on Applied Mathematics and Computation, 2022, 4(3): 823-854.
[15]	Nils Gerhard, Siegfried Müller, Aleksey Sikstel. A Wavelet-Free Approach for Multiresolution-Based Grid Adaptation for Conservation Laws [J]. Communications on Applied Mathematics and Computation, 2022, 4(1): 108-142.

My Way: A Computational Autobiography

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments