메뉴 건너뛰기




Volumn 40, Issue 5, 2002, Pages 1716-1762

Simulation of the solution of a viscous porous medium equation by a particle method

Author keywords

Many particle systems; Particle methods; Smoothed particle hydrodynamics

Indexed keywords

APPROXIMATION THEORY; BROWNIAN MOVEMENT; COMPUTER SIMULATION; COMPUTER SOFTWARE; ERROR ANALYSIS; HYDRODYNAMICS; MATHEMATICAL MODELS; POROUS MATERIALS; PROBABILITY DENSITY FUNCTION;

EID: 0345327708     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142900363377     Document Type: Article
Times cited : (7)

References (18)
  • 1
    • 0001461058 scopus 로고
    • The equations of motion of particles in smoothed particle hydrodynamics
    • G. V. BICKNELL, The equations of motion of particles in smoothed particle hydrodynamics, SIAM J. Sci. Statist. Comput., 12 (1991), pp. 1198-1206.
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 1198-1206
    • Bicknell, G.V.1
  • 2
    • 0031539944 scopus 로고    scopus 로고
    • A stochastic particle method for the McKean-Vlasov and the Burgers equation
    • M. BOSSY AND D. TALAY, A stochastic particle method for the McKean-Vlasov and the Burgers equation, Math. Comp., 66 (1997), pp. 157-192.
    • (1997) Math. Comp. , vol.66 , pp. 157-192
    • Bossy, M.1    Talay, D.2
  • 3
    • 0010988086 scopus 로고
    • A stochastic simulation for solving scalar reaction-diffusion equations
    • B. CHAUVIN AND A. ROUAULT, A stochastic simulation for solving scalar reaction-diffusion equations, Adv. in Appl. Probab., 22 (1990), pp. 88-100.
    • (1990) Adv. in Appl. Probab. , vol.22 , pp. 88-100
    • Chauvin, B.1    Rouault, A.2
  • 4
    • 35949018172 scopus 로고
    • Particle simulation of plasmas
    • J. M. DAWSON, Particle simulation of plasmas, Rev. Modern Phys., 55 (1983), pp. 403-447.
    • (1983) Rev. Modern Phys. , vol.55 , pp. 403-447
    • Dawson, J.M.1
  • 5
    • 33645123735 scopus 로고
    • Kernel estimates as a basis for general particle methods in hydrodynamics
    • R. A. GINGOLD AND J. J. MONAGHAN, Kernel estimates as a basis for general particle methods in hydrodynamics, J. Comput. Phys., 46 (1982), pp. 429-453.
    • (1982) J. Comput. Phys. , vol.46 , pp. 429-453
    • Gingold, R.A.1    Monaghan, J.J.2
  • 6
    • 0011558848 scopus 로고    scopus 로고
    • The numerical analysis of random particle methods applied to Vlasov-Poisson-Fokker-Planck kinetic equations
    • K. J. HAVLAK AND H. D. VICTORY, JR., The numerical analysis of random particle methods applied to Vlasov-Poisson-Fokker-Planck kinetic equations, SIAM J. Numer. Anal., 33 (1996), pp. 291-317.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 291-317
    • Havlak, K.J.1    Victory Jr., H.D.2
  • 10
    • 84968499110 scopus 로고
    • Convergence of the random vortex method in two dimensions
    • D.-G. LONG, Convergence of the random vortex method in two dimensions, J. Amer. Math. Soc., 1 (1988), pp. 779-804.
    • (1988) J. Amer. Math. Soc. , vol.1 , pp. 779-804
    • Long, D.-G.1
  • 11
    • 8444240793 scopus 로고
    • Particle Methods for the Boltzmann Equation
    • Cambridge University Press, Cambridge, UK
    • H. NEUNZERT AND J. STRUCKMEIER, Particle Methods for the Boltzmann Equation, Acta Numer., Cambridge University Press, Cambridge, UK, 1995, pp. 417-457.
    • (1995) Acta Numer. , pp. 417-457
    • Neunzert, H.1    Struckmeier, J.2
  • 12
    • 51249177449 scopus 로고
    • A law of large numbers for moderately interacting diffusion processes
    • K. OELSCHLÄGER, A law of large numbers for moderately interacting diffusion processes, Z. Wahrsch. Verw. Gebiete, 69 (1985), pp. 279-322.
    • (1985) Z. Wahrsch. Verw. Gebiete , vol.69 , pp. 279-322
    • Oelschläger, K.1
  • 13
    • 0010182615 scopus 로고
    • A fluctuation theorem for moderately interacting diffusion processes
    • K. OELSCHLÄGER, A fluctuation theorem for moderately interacting diffusion processes, Probab. Theory Related Fields, 74 (1987), pp. 591-616.
    • (1987) Probab. Theory Related Fields , vol.74 , pp. 591-616
    • Oelschläger, K.1
  • 14
    • 0005500243 scopus 로고
    • On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes
    • K. OELSCHLÄGER, On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes, Probab. Theory Related Fields, 82 (1989), pp. 565-586.
    • (1989) Probab. Theory Related Fields , vol.82 , pp. 565-586
    • Oelschläger, K.1
  • 15
    • 0000980444 scopus 로고
    • On the connection between Hamiltonian many-particle systems and the hydrodynamical equations
    • K. OELSCHLÄGER, On the connection between Hamiltonian many-particle systems and the hydrodynamical equations, Arch. Rational Mech. Anal., 115 (1991), pp. 297-310.
    • (1991) Arch. Rational Mech. Anal. , vol.115 , pp. 297-310
    • Oelschläger, K.1
  • 16
    • 25944462292 scopus 로고
    • The description of many-particle systems by the equations for a viscous, compressible, barotropic fluid
    • K. OELSCHLÄGER, The description of many-particle systems by the equations for a viscous, compressible, barotropic fluid, Math. Models Methods Appl. Sci., 5 (1995), pp. 887-922.
    • (1995) Math. Models Methods Appl. Sci. , vol.5 , pp. 887-922
    • Oelschläger, K.1
  • 17
    • 25944476744 scopus 로고    scopus 로고
    • A sequence of integro-differential equations approximating a viscous porous medium equation
    • K. OELSCHLÄGER, A sequence of integro-differential equations approximating a viscous porous medium equation, Z. Anal. Anwendungen, 20 (2001), pp. 55-91.
    • (2001) Z. Anal. Anwendungen , vol.20 , pp. 55-91
    • Oelschläger, K.1
  • 18
    • 84966244969 scopus 로고
    • xx + u(1 - u)
    • xx + u(1 - u), Math. Comp., 52 (1989), pp. 615-645.
    • (1989) Math. Comp. , vol.52 , pp. 615-645
    • Puckett, E.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.