xx IDScalarWave

IDScalarWave

Gabrielle Allen Horst Beyer

Date

Abstract

Initial Data for the 3D Scalar Wave Equation

1 Purpose This thorn provides different initial data for the 3D scalar wave equation.

2 Spherically Symmetric Solutions

The general spherically symmetric solution can be written where the functions and can be freely chosen.

Making the additional requirement of time symmetry at , forces Thus if the solution at t=0 is given by , the general solution will be

3 Gaussian

The gaussian solution is spherically symmetric about the origin of the Cartesian coordinate system, and is time symmetric. The initial profile is with the solution at the origin being

The Gaussian solution is set with the parameters

     amplitude =

     sigma =

4 Parameters

11amplitude10Scope: privatex01  REAL

11Description: The amplitude of the waves

11 Range 10 x01 Default: 1.0
11*:*  10No restriction

11

11kx  10Scope: privatex01  REAL

11Description: The wave number in the x-direction

11 Range 10 x01 Default: 4.0
11*:*  10No restriction

11ky  10Scope: privatex01  REAL

11Description: The wave number in the y-direction

11 Range 10 x01 Default: 0.0
11*:*  10No restriction

11

11kz  10Scope: privatex01  REAL

11Description: The wave number in the z-direction

11 Range 10 x01 Default: 0.0
11*:*  10No restriction

11

11radius 10Scope: privatex01  REAL

11Description: The radius of the gaussian wave

11 Range 10 x01 Default: 0.0
110:*  10Positive

11

11sigma 10Scope: privatex01  REAL

11Description: The sigma for the gaussian wave

11 Range 10 x01 Default: 0.1
110:*  10Positive

11

11initialxdata 10Scope: restrictedx01  KEYWORD

11Description: Type of initial data

11 Range 10 x01 Default: gaussian
11plane  10Plane wave
11gaussian 10Gaussian wave
11box  10Box wave
11none  10No initial data, zero phi

11

11type  10Scope: shared from GRIDx01KEYWORD

11

5 Interfaces

General Implements: idscalarwave

Inherits: wavetoy grid 6 Schedule This section lists all the variables which are assigned storage by thorn CactusWave/IDScalarWave. Storage can either last for the duration of the run (Always means that if this thorn is activated storage will be assigned, Conditional means that if this thorn is activated storage will be assigned for the duration of the run if some condition is met), or can be turned on for the duration of a schedule function.

Storage NONE

Scheduled Functions

CCTKxPARAMCHECK x idscalarwavexcheckparameters x check parameters x

11x11Language:11fortran
11 x 11Type: 11function

11

CCTKxINITIAL x wavetoyxinitialdata x execute initial data for wavetoy x

11x11Type:11group

11

WaveToyxInitialData x idscalarwavexinitialdata x initial data for 3d wave equation x

11x11Language:11fortran
11 x 11Storage: 11wavetoy::scalarevolve[3]
11 x 11Type: 11function