This paper considers an inverse problem for a partial differential equation to identify a pollution point source in a watershed. The mathematical model of the problem is a weakly coupled system of two linear parabolic...This paper considers an inverse problem for a partial differential equation to identify a pollution point source in a watershed. The mathematical model of the problem is a weakly coupled system of two linear parabolic equations for the concentrations u（x, t） and v（x, t） with an unknown point source F（x, t） = A（ t）δ（x- s） related to the concentration u（x, t）, where s is the point source location and A（t） is the amplitude of the pollution point source. Assuming that source F becomes inactive after time T＊, it is proved that it can be uniquely determined by the indirect measurements { v（0, t）, v（ a, t）, v（ b, t）, v（ l, t）, 0 〈 t ≤ T, T＊ 〈 T}, and, thus, the local Lipschitz stability for this inverse source problem is obtained. Based on the proof of its uniqueness, an inversion scheme is presented to determine the point source. Finally, two numerical examples are given to show the feasibility of the inversion scheme.展开更多
Performances and efficiencies of displacement ventilation(DV) and partial ventilation(PV) for industrial halls of different configurations as well as the heat and mass transports within the industrial halls were numer...Performances and efficiencies of displacement ventilation(DV) and partial ventilation(PV) for industrial halls of different configurations as well as the heat and mass transports within the industrial halls were numerically investigated. Three levels of Rayleigh number(5.8×1010, 1.0×1012 and 2.1×1012) and two values of source contaminant flux(5 mg/s and 50 mg/s) were considered. The inlet Reynolds numbers were 2×104, 5×104, 1.5×105 and 4.5×105 for DV and 5×105, 1×106, 2×106 and 4×106 for PV, respectively. From the results, it is concluded that the above parameters have very complex impacts on the conjugated heat and mass transports. From points of view of acceptable indoor air quality and ventilation efficiency, PV at Re=1×106 with side-located sources and 65% of the supply air extracted through floor level outlets is the best choice when Ra=5.8×1010. However, DVs at Re=5×104 and Re=1.5×105with center-located sources and floor-mounted air suppliers are the best choices for Ra=1.0×1012 and Ra=2.1×1012, respectively. When source contaminant flux reaches 50 mg/s, local extraction as a supplement of general ventilation is recommended. The results can be a first approximation to 3D numerical investigation and preliminary ventilation system design guidelines for high-rise industrial halls.展开更多
基金The National Natural Science Foundation of China(No.10861001)the Natural Science Foundation of Jiangxi Province
文摘This paper considers an inverse problem for a partial differential equation to identify a pollution point source in a watershed. The mathematical model of the problem is a weakly coupled system of two linear parabolic equations for the concentrations u（x, t） and v（x, t） with an unknown point source F（x, t） = A（ t）δ（x- s） related to the concentration u（x, t）, where s is the point source location and A（t） is the amplitude of the pollution point source. Assuming that source F becomes inactive after time T＊, it is proved that it can be uniquely determined by the indirect measurements { v（0, t）, v（ a, t）, v（ b, t）, v（ l, t）, 0 〈 t ≤ T, T＊ 〈 T}, and, thus, the local Lipschitz stability for this inverse source problem is obtained. Based on the proof of its uniqueness, an inversion scheme is presented to determine the point source. Finally, two numerical examples are given to show the feasibility of the inversion scheme.
基金Project(2011BAJ03B07)supported by National Twelve Five-year Science and Technology Support Program of ChinaProject supported by the China Scholarship Council+1 种基金Project(51276057,51376198)supported by the National Natural Science Foundation of ChinaProject(CX2014B064)supported by Hunan Provincial Innovation Foundation for Postgraduate,China
文摘Performances and efficiencies of displacement ventilation(DV) and partial ventilation(PV) for industrial halls of different configurations as well as the heat and mass transports within the industrial halls were numerically investigated. Three levels of Rayleigh number(5.8×1010, 1.0×1012 and 2.1×1012) and two values of source contaminant flux(5 mg/s and 50 mg/s) were considered. The inlet Reynolds numbers were 2×104, 5×104, 1.5×105 and 4.5×105 for DV and 5×105, 1×106, 2×106 and 4×106 for PV, respectively. From the results, it is concluded that the above parameters have very complex impacts on the conjugated heat and mass transports. From points of view of acceptable indoor air quality and ventilation efficiency, PV at Re=1×106 with side-located sources and 65% of the supply air extracted through floor level outlets is the best choice when Ra=5.8×1010. However, DVs at Re=5×104 and Re=1.5×105with center-located sources and floor-mounted air suppliers are the best choices for Ra=1.0×1012 and Ra=2.1×1012, respectively. When source contaminant flux reaches 50 mg/s, local extraction as a supplement of general ventilation is recommended. The results can be a first approximation to 3D numerical investigation and preliminary ventilation system design guidelines for high-rise industrial halls.
