PhD Thesis - staffweb - University of Greenwich

APPENDIX 4 : SMARTFIRE TECHNICAL REFERENCE GUIDEThe previously mentioned approximations are based on a typical control volume arrangementas depicted above. This is a typical 2D Control Volume set-up. Th e computational moleculeshows the influence of neighbouring control volumes (North, South, West and East) on thecontrol volume of interest (labelled P). It should be noted that SMARTFIRE actually uses a3D unstructured mesh but similar concepts apply.1.2.1.1 Transient TermThe transient term is approximated using the backward difference technique. This gives∫ ∫0 0∂ ( ρφ)VPρPφP− VPρPφdV dt ≅∂tt0tPt −∆t V ∆(9a)1.2.1.2 Convection TermThe convection term is the most important term in the equation. Care must be taken inapproximating this term, as inappropriate approximations can lead to large error s orinstability problems if not handled with care. Th is givesAppendix 11.4 Page 144-11 11