New least squares method with geometric conservation law (GC-LSM) for compressible flow computation in meshless method

Computers and Fluids

Volumn 172, Issue , 2018, Pages 122-146

  Huh, Jin Young ^a   Rhee, Jae Sang ^a   Kim, Kyu Hong ^a   Jung, Suk Young ^b  

^a Seoul National University   (South Korea)

^b Agency for Defence Development   (South Korea)

Author keywords

AUSMPW+; GC LSM; Geometric conservation law; Least squares method; Meshless method; MUSCL limiters

Indexed keywords

COMPRESSIBLE FLOW; FINITE VOLUME METHOD; GEOMETRY; HYPERSONIC FLOW; LAGRANGE MULTIPLIERS; OSCILLATING FLOW; PHYSICAL PROPERTIES;

AUSMPW; GC-LSM; GEOMETRIC CONSERVATION LAWS; LEAST SQUARES METHODS; MESH-LESS METHODS;

LEAST SQUARES APPROXIMATIONS;

EID: 85049808887     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2018.06.010     Document Type: Article

References (26)

1. Kim, S.H., Huh, J.Y., Park, J.H., Kim, K.H., Jung, S.Y., A meshless point generation technique using octrees for unsteady flow around bodies with relative motion. Proceedings of the Asia-pacific international symposium on aerospace technology, Seoul, Korea, 2017.
2. Nguyen, V.P., Tabczuk, T., Bordas, S., Duflot, M., Meshless methods: a review and computer implementation aspects. Math Comput Simul 79 (2008), 763–813.
3. Shepard, D., A two-dimensional function for irregularly spaced points. Proceedings of the twenty third ACM national conference, 1968, 517–524.
4. Lancaster, P., Salkauskas, K., Surfaces generated by moving least squares methods. Math Comput 37 (1981), 141–158.
5. Sridar, D., Balakrishnan, N., An upwind finite difference scheme for meshless solvers. J Comput Phys 189 (2003), 1–29.
6. A.K. Ghosh, S.M. Deshpande. Least squares kinetic upwind method for inviscid compressible flows. AIAA Paper95-1735, 1995.
7. J.T. Batina. A gridless Euler/Navier–Stokes solution algorithm for complex aircraft applications. AIAA Paper93-0333, 1993.
8. Praveen, C., Deshpande, S.M., Kinetic meshless method for compressible flows. Int J Numer Methods Fluids 55 (2007), 1059–1089.
9. Katz, A., Jameson, A., A meshless volume scheme. AIAA 2009-3534. Proceedings of the ninteenth AIAA computational fluid dynamics, San Antonio, Texas, 2009.
10. Katz, A., Jameson, A., Meshless scheme based on alignment constraints. AIAA J 48:11 (2010), 2501–2511.
11. Chen, H.Q., Shu, C., An efficient implicit mesh-free method to solve two-dimensional compressible Euler equations. Int J Modern Phys C 16:3 (2005), 439–454.
12. Shu, C., Ding, H., Chen, H.Q., Wang, T.G., An upwind local RBF-DQ method for simulation of inviscid compressible flows. Comput Methods Appl Mech Eng 194 (2005), 2001–2017.
13. Chiu, E.K-Y., Wang, Q., Hu, R., Jameson, A., A conservative mesh-free scheme and generalized framework for conservation laws. SIAM J Sci Comput 34:6 (2012), A2896–A2916.
14. Kim, K., Kim, C., Rho, O., Methods for the accurate computations of hypersonic flows I. AUSMPW+ Scheme. J Comput Phys 174 (2001), 38–80.
15. Sweby, P.K., High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J Numer Anal 21:5 (1984), 995–1011.
16. Harten, A., High resolution schemes for hyperbolic conservation laws. J Comput Phys 49:3 (1983), 357–393.
17. Katz, A., Jameson, A., A comparison of various meshless schemes within a unified algorithm, AIAA 2009-596. Proceedings of the forty seventh AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, Orlando, Florida, 2009.
18. Jameson, A., Analysis and design of numerical schemes for gas dynamics 1 artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence. Int J Comput Fluid Dyn 4 (1995), 171–218.
19. Yoon, S., Jameson, A., Lower-upper symmetric-gauss-seidel method for the Euler and Navier–Stokes equations. AIAA J 26:9 (1988), 1025–1026.
20. http://www.grc.nasa.gov/WWW/wind/valid/cdv/cdv.html.
21. M.S. Liou. A generalized procedure for constructing an upwind-based TVD scheme. AIAA Paper 87-0355, (Also NASA TM 88926) 1987.
22. J.W. Slater, J.C. Dudek, and K.E. Tatum. The NPARC verification and validation archive. ASME Paper 2000-FED-11233, (Also NASA TM-2000-209946) 2000.
23. Ambrosio, A., Wortman, A., Stagnation-Point shock-detachment distance for flow around spheres and cylinders in air. J Aerosp Sci, 29(7), 1962 875-875.
24. Rhee, J., Huh, J., Kim, K., Jung, S., Three dimensional meshless point generation technique for complex geometry. Proceedings of the world congress on advances in structural engineering and mechanics aeronautics, nano, bio, robotics, and energy, Incheon, Korea, 2015.
25. Mc Ghee, R.J., Jet-plume-induced flow separation on axisymmetric bodies at Mach number of 3.00, 4.5, and 6.00. NASA TM X-2059., 1970, NASA Langley Research Center.
26. Burt, J.R. Jr., An investigation of the effectiveness of several devices in simulating a rocket plume at free stream Mach numbers 0.9 to 1.2 (No. RD-TR-71-22)., 1971, Army Missile Command Redstone Arsenal Ala Aeroballistics Directorate.