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References

1
P. ARMINJON, D. STANESCU & M.-C. VIALLON, A Two-Dimensional Finite Volume Extension of the Lax-Friedrichs and Nessyahu-Tadmor Schemes for Compressible Flow, (1995), preprint.

2
P. ARMINJON, D. STANESCU & M.-C. VIALLON, A two-dimensional finite volume extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for compressible flows, Preprint.

3
P. ARMINJON & M.-C. VIALLON, Généralisation du Schéma de Nessyahu-Tadmor pour Une Équation Hyperbolique à Deux Dimensions D'espace, C.R. Acad. Sci. Paris, t. 320 , série I. (1995), pp. 85-88.

4
F. BEREUX & L. SAINSAULIEU, A Roe-type Riemann Solver for Hyperbolic Systems with Relaxation Based on Time-Dependent Wave Decomposition, Numer. Math,. 77, (1997), pp. 143-185.

5
D. L. BROWN & M. L. MINION Performance of under-resolved two-dimensional incompressible flow simulations, J. Comp. Phys. 122, (1985) 165-183.

6
P. COLELLA & P. WOODWARD, The piecewise parabolic method (PPM) for gas-dynamical simulations, JCP 54, 1984, pp. 174-201.

7
B. ENGQUIST & O. RUNBORG, Multi-phase computations in geometrical optics, J. Comp. Appl. Math., 1996, in press.

8
ERBES, A high-resolution Lax-Friedrichs scheme for Hyperbolic conservation laws with source term. Application to the Shallow Water equations. Preprint.

9
K.O. FRIEDRICHS & P.D. LAX, Systems of Conservation Equations with a Convex Extension, Proc. Nat. Acad. Sci., 68, (1971), pp.1686-1688.

10
E. GODLEWSKI & P.-A. RAVIART, Hyperbolic Systems of Conservation Laws, Mathematics & Applications, Ellipses, Paris, 1991.

11
S.K. GODUNOV, A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics, Mat. Sb. 47, 1959, pp. 271-290.

12
A. HARTEN, High Resolution Schemes for Hyperbolic Conservation Laws, JCP, 49, (1983), pp.357-393.

13
A. HARTEN, B. ENGQUIST, S. OSHER & S.R. CHAKRAVARTHY, Uniformly high order accurate essentially non-oscillatory schemes. III, JCP 71, 1982, pp. 231-303.

14
HUYNH, A piecewise-parabolic dual-mesh method for the Euler equations, AIAA-95-1739-CP, The 12th AIAA CFD Conf., 1995.

15
G.-S. JIANG, D. LEVY, C.-T. LIN, S. OSHER & E. TADMOR, High-resolution Non-Oscillatory Central Schemes with Non-Staggered Grids for Hyperbolic Conservation Laws, SIAM Journal on Num. Anal., to appear.

16
G.-S JIANG & E. TADMOR, Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws, SIAM J. Scie. Comp., to appear.

17
S. JIN, private communication.

18
S. JIN AND Z. XIN, The relaxing schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math. 48 (1995) 235-277.

19
B. VAN LEER, Towards the Ultimate Conservative Difference Scheme, V. A Second-Order Sequel to Godunov's Method, JCP, 32, (1979), pp.101-136.

20
R. KUPFERMAN, Simulation of viscoelastic fluids: Couette-Taylor flow, J. Comp. Phys., to appear.

21
R. KUPFERMAN, A numerical study of the axisymmetric Couette-Taylor problem using a fast high-resolution second-order central scheme, SIAM. J. Sci. Comp., to appear.

22
R. KUPFERMAN & E. TADMOR, A Fast High-Resolution Second-Order Central Scheme for Incompressible Flow s, Proc. Nat. Acad. Sci.,

23
R.J. LEVEQUE, Numerical Methods for Conservation Laws, Lectures in Mathematics, Birkhauser Verlag, Basel, 1992.

24
D. LEVY, Third-order 2D Central Schemes for Hyperbolic Conservation Laws, in preparation.

25
D. LEVY & E. TADMOR, Non-oscillatory Central Schemes for the Incompressible 2-D Euler Equations, Math. Res. Let., 4, (1997), pp.321-340.

26
D. LEVY & E. TADMOR, Non-oscillatory boundary treatmentfor staggered central schemes, preprint.

27
X.-D. LIU & P. D. LAX, Positive Schemes for Solving Multi-dimensional Hyperbolic Systems of Conservation Laws, Courant Mathematics and Computing Laboratory Report, Comm. Pure Appl. Math.

28
X.-D. LIU & S. OSHER, Nonoscillatory High Order Accurate Self-Similar Maximum Principle Satisfying Shock Capturing Schemes I, SINUM, 33, no. 2 (1996), pp.760-779.

29
X.-D. LIU & E. TADMOR, Third Order Nonoscillatory Central Scheme for Hyperbolic Conservation Laws, Numer. Math., to appear.

30
H. NESSYAHU, Non-oscillatory second order central type schemes for systems of nonlinear hyperbolic conservation laws, M.Sc. Thesis, Tel-Aviv University, 1987.

31
H. NESSYAHU & E. TADMOR, Non-oscillatory Central Differencing for Hyperbolic Conservation Laws, JCP, 87, no. 2 (1990), pp.408-463.

32
H. NESSYAHU, E. TADMOR & T. TASSA, On the convergence rate of Godunov-type schemes, SINUM 31, 1994, pp. 1-16.

33
S. OSHER & E. TADMOR, On the Convergence of Difference Approximations to Scalar Conservation Laws, Math. Comp., 50, no. 181 (1988), pp.19-51.

34
P. L. ROE, Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes, JCP, 43, (1981), pp.357-372.

35
A. ROGERSON & E. MEIBURG, A numerical study of the convergence properties of ENO schemes, J. Sci. Comput., 5, 1990, pp. 127-149.

36
O. RUNBORG, Multiphase Computations in Geometrical Optics, UCLA CAM report no. 96-52 (1996).

37
V. ROMANO & G. RUSSO, Numerical solution for hydrodynamical models of semiconductors, IEEE, to appear.

38
A.M. ANILE, V. ROMANO & G. RUSSO, Extended hydrodymnamical model of carrier transport in semiconductors, Phys. Rev. B., to appear.

39
F. BIANCO, G. PUPPO & G. RUSSO, High order central schemes for hyperbolic systems of conservation laws, SIAM J. Sci. Comp., to appear.

40
R. SANDERS, A Third-order Accurate Variation Nonexpansive Difference Scheme for Single Conservation Laws, Math. Comp., 41 (1988), pp.535-558.

41
R. SANDERS R. & A. WEISER, A High Resolution Staggered Mesh Approach for Nonlinear Hyperbolic Systems of Conservation Laws, JCP, 1010 (1992), pp.314-329.

42
P. K. SWEBY, High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws, SINUM, 21, no. 5 (1984), pp.995-1011.

43
C.-W. SHU, Numerical experiments on the accuracy of ENO and modified ENO schemes, JCP 5, 1990, pp. 127-149.

44
G. SOD, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, JCP 22, 1978, pp. 1-31.

45
E. TADMOR & C.C. WU, Central Scheme for the Multidimensional MHD Equations, in preparation.

46
P. WOODWARD & P. COLELLA, The numerical simulation of two-dimensional fluid flow with strong shocks, JCP 54, 1988, pp. 115-173.



Eitan Tadmor
Mon Dec 8 17:34:34 PST 1997