Absorbing boundary conditions for the numerical simulation of waves

Authors:
Bjorn Engquist and Andrew Majda

Journal:
Math. Comp. **31** (1977), 629-651

MSC:
Primary 65M05; Secondary 65N99

DOI:
https://doi.org/10.1090/S0025-5718-1977-0436612-4

MathSciNet review:
0436612

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In practical calculations, it is often essential to introduce artificial boundaries to limit the area of computation. Here we develop a systematic method for obtaining a hierarchy of local boundary conditions at these artificial boundaries. These boundary conditions not only guarantee stable difference approximations but also minimize the (unphysical) artificial reflections which occur at the boundaries.

**[1]**Heinz-Otto Kreiss,*Initial boundary value problems for hyperbolic systems*, Comm. Pure Appl. Math.**23**(1970), 277–298. MR**0437941**, https://doi.org/10.1002/cpa.3160230304**[2]**Andrew Majda and Stanley Osher,*Reflection of singularities at the boundary*, Comm. Pure Appl. Math.**28**(1975), no. 4, 479–499. MR**0492792**, https://doi.org/10.1002/cpa.3160280404

Andrew Majda and Stanley Osher,*Erratum: “Reflection of singularities at the boundary” (Comm. Pure Appl. Math. 28 (1975), no. 4, 479–499)*, Comm. Pure Appl. Math.**28**(1975), no. 5, 677. MR**0492793**, https://doi.org/10.1002/cpa.3160280504**[3]**Louis Nirenberg,*Lectures on linear partial differential equations*, American Mathematical Society, Providence, R.I., 1973. Expository Lectures from the CBMS Regional Conference held at the Texas Technological University, Lubbock, Tex., May 22–26, 1972; Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 17. MR**0450755****[4]**Michael E. Taylor,*Reflection of singularities of solutions to systems of differential equations*, Comm. Pure Appl. Math.**28**(1975), no. 4, 457–478. MR**0509098**, https://doi.org/10.1002/cpa.3160280403**[5]**Jeffrey B. Rauch and Frank J. Massey III,*Differentiability of solutions to hyperbolic initial-boundary value problems*, Trans. Amer. Math. Soc.**189**(1974), 303–318. MR**0340832**, https://doi.org/10.1090/S0002-9947-1974-0340832-0**[6]**DAVID M. BOORE, "Finite difference methods for seismic wave propagation in heterogeneous materials,"*Methods of Comp. Physics (Seismology)*, v. 11, 1972, pp. 1-37.**[7]**K. R. Kelly, R. M. Alford, S. Treitel, and R. W. Ward,*Application of finite difference methods to exploration seismology*, Topics in numerical analysis, II (Proc. Roy. Irish Acad. Conf., Univ. College, Dublin, 1974) Academic Press, London, 1975, pp. 57–76. MR**0408753****[8]**Patrick J. Roache,*Computational fluid dynamics*, Hermosa Publishers, Albuquerque, N.M., 1976. With an appendix (“On artificial viscosity”) reprinted from J. Computational Phys. 10 (1972), no. 2, 169–184; Revised printing. MR**0411358****[9]**T. ELVIUS & A. SUNDSTRÖM, "Computationally efficient schemes and boundary conditions for a fine mesh barotropic model based on the shallow water equations,"*Tellus*, v. 25, 1973, pp. 132-156.**[10]**E. L. LINDMAN, "Free space boundary conditions for the time dependent wave equation,"*J. Computational Phys.*, v. 18, 197S, pp. 66-78.**[11]**I. ORLANSKI, "A simple boundary condition for unbounded hyperbolic flows,"*J. Computational Phys.*, v. 21, 1976, pp. 251-269.**[12]**M. E. HANSON & A. G. PETSCHEK, "A boundary condition for sufficiently reducing boundary reflection with a Lagrangian mesh,"*J. Computational Phys.*, v. 21, 1976, pp. 333-339.**[13]**W. D. SMITH, "A nonreflecting plane boundary for wave propagation problems,"*J. Computational Phys.*, v. 15, 1974, pp. 492-503.

Retrieve articles in *Mathematics of Computation*
with MSC:
65M05,
65N99

Retrieve articles in all journals with MSC: 65M05, 65N99

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0436612-4

Article copyright:
© Copyright 1977
American Mathematical Society