Changes between Version 40 and Version 41 of ModulesOnAstroBear
- Timestamp:
- 01/23/13 07:29:20 (12 years ago)
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ModulesOnAstroBear
v40 v41 103 103 There are two major data arrays in {{{InfoDef}}}: the {{{q}}} array and the {{{aux}}} array. {{{q}}} holds the volume averaged data and is used by all AstroBEAR simulations while {{{aux}}} holds face averaged data and is used only for MHD when nDim > 1. Note that volume averaged data and cell-centered data are often used interchangeably, but there is an important distinction. Take for instance a simple function f(x) defined on the interval [0:h]. The average of f(x) over the interval is 104 104 105 f(0)+d,,1,,f(0)h/2+d,,2,,f(0)h^2^/ 3+...105 f(0)+d,,1,,f(0)h/2+d,,2,,f(0)h^2^/6+... 106 106 107 107 where the cell centered value is 108 108 109 f(0)+d,,1,,f(0)h/2+d,,2,,f(0)h^2^/ 6+...109 f(0)+d,,1,,f(0)h/2+d,,2,,f(0)h^2^/8+... 110 110 111 111 so the cell centered value is second order accurate for the volume average and usually is a quick way to estimate the volume average. However if the function has large 2nd derivatives (or higher) this can lead to large errors in the volume average. This is often apparent when modeling discontinuities along curved boundaries. There are two ways to handle this problem:
