3D Finite Volume simulation of acoustic waves in the earth atmosphere

Abstract We present a very high-order Finite Volume discretization of the 3D linearized convective Euler equations for the simulation of acoustic waves in the Earth atmosphere. We also derive a weakly nonlinear model for the approximation of N-waves. We discuss the use and the implementation of these methods on massively parallel computers based on our experience on the Bull-TERA 10 parallel HPC machine at the CEA. Verification–validation is done in dimension two and three with physical data obtained from a large-scale physical experiment.

[1]  François Coulouvrat,et al.  Nonlinear focusing of acoustic shock waves at a caustic cusp. , 2005, The Journal of the Acoustical Society of America.

[2]  J. Lighthill,et al.  An Informal Introduction to Theoretical Fluid Mechanics , 1986 .

[3]  M. Dumbser,et al.  Multiple-scale modelling of acoustic sources in low Mach-number flow , 2005 .

[4]  Eleuterio F. Toro,et al.  ADER schemes for three-dimensional non-linear hyperbolic systems , 2005 .

[5]  C. Bailly,et al.  Numerical Solution of Acoustic Propagation Problems Using linearized Euler's Equations* , 2000 .

[6]  J. Noble,et al.  Benchmark cases for outdoor sound propagation models , 1995 .

[7]  C. Bogey,et al.  Computation of Flow Noise Using Source Terms in Linearized Euler's Equations , 2000 .

[8]  P. Raviart,et al.  Numerical Approximation of Hyperbolic Systems of Conservation Laws , 1996, Applied Mathematical Sciences.

[9]  Bruno Desprésaff n.  Finite volume transport schemes , 2008 .

[10]  F. Coulouvrat,et al.  Numerical Simulation of Sonic Boom Focusing , 2002 .

[11]  François Coulouvrat,et al.  Sonic boom in the shadow zone: A geometrical theory of diffraction , 2002 .

[12]  Eleuterio F. Toro,et al.  ADER schemes for scalar non-linear hyperbolic conservation laws with source terms in three-space dimensions , 2005 .

[13]  G. Strang.  Introduction to Linear Algebra , 1993 .

[14]  Stéphane Del Pino,et al.  Arbitrary high-order schemes for the linear advection and wave equations: application to hydrodynamics and aeroacoustics , 2006 .

[15]  Patrick Joly,et al.  Construction and analysis of higher order finite difference schemes for the 1D wave equation , 2000 .

[16]  Christian Tenaud,et al.  High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations , 2004 .

[17]  C. Tam,et al.  Dispersion-relation-preserving finite difference schemes for computational acoustics , 1993 .