CHARACTERISTIC GALERKIN METHODS FOR SCALAR CONSERVATION-LAWS IN ONE DIMENSION

被引：25

作者：

CHILDS, PN ^{[1
]}

MORTON, KW ^{[1
]}

机构：

[1] UNIV OXFORD, NUMER ANAL GRP, COMP LAB, OXFORD OX1 3QD, ENGLAND

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 1990年 / 27卷 / 03期

关键词：

D O I：

10.1137/0727035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A general formulation of the Euler characteristic Galerkin (ECG) technique is given for scalar conservation laws, from which specific algorithms are derived and analysed. These are developed from piecewise constant approximation. The basic first-order scheme is then Brenier's extension of the Engquist-Osher method; but adaptive recovery techniques are used to resolve discontinuities accurately and give second-order accuracy for smooth flows. Convergence is proved for convex flux functions, nonuniform meshes, and arbitrary timesteps, under conditions that can be readily met by the recovery procedures.

引用

页码：553 / 594

页数：42

共 44 条

[1]

Bardos C., 1979, COMM PART DIFF EQN, V4, P1017, DOI DOI 10.1080/03605307908820117

[2]

Benque J., 1982, 4 INT S FIN EL FLOW, P295

[3]

BERCOVIER M, 1982, P C MATH FIN EL APPL, V4, P471

[4]

Boris J. P., 1975, J COMPUT PH, V18, P248, DOI DOI 10.1016/0021-9991(75)90002-9

[5] FLUX-CORRECTED TRANSPORT .1. SHASTA, A FLUID TRANSPORT ALGORITHM THAT WORKS [J].

BORIS, JP ;

BOOK, DL .

JOURNAL OF COMPUTATIONAL PHYSICS, 1973, 11 (01) :38-69

[6] AVERAGED MULTIVALUED SOLUTIONS FOR SCALAR CONSERVATION-LAWS [J].

BRENIER, Y .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1984, 21 (06) :1013-1037

[7] Mechanism of fluid displacement in sands [J].

Buckley, SE ;

Leverett, MC .

TRANSACTIONS OF THE AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS, 1942, 146 :107-116

[8]

CHILDS PM, 1986, 865 OXF U COMP LAB N

[9]

CHILDS PM, 1988, THESIS U OXFORD OXFO

[10] THE PIECEWISE PARABOLIC METHOD (PPM) FOR GAS-DYNAMICAL SIMULATIONS [J].

COLELLA, P ;

WOODWARD, PR .

JOURNAL OF COMPUTATIONAL PHYSICS, 1984, 54 (01) :174-201

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