A multi-heat source ring-shaped heat-supply network is not a plane net and supply-return pipe net is dissymmetric under faulty condition. We present a method for topology structure of spatial heat-supply network based on graph theory. With object-oriented programming,it defines graph and includes correlation arithmetic according to basic structure information of supply-return pipe net and builds incidence matrix and fundamental circuit matrix automatically. It creates a spatial heat-supply network "tree"which includes information of heat source and heat users and adopts breadth-first search based on plane graph. According the tree,basic incidence matrix and fundamental circuit matrix of spatial heat-supply network are established. In simulating heating network of Harbin development zone,a program of multi-heat source ring-shaped heat-supply network in topology structure is build and computing performance is verified. It provides a method for complex heat-supply network hydrodynamic condition analysis and dissymmetric heatsupply network calculation based on arithmetic of graph and adapts to various model pipe nets.

A uniform method for unsteady flows at arbitrary Mach number is developed.The preconditioned dual-time compressible Navier-Stokes equations for unsteady flows are obtained by incorporating a pseudo-time derivative term and preconditioning.The inviscid flux vectors and the viscous flux vectors are differentiated by a Roe-scheme of three-order and a general central difference scheme,respectively.A pseudo-time subiteration with an implicit ADI-LU scheme is implemented based on state-vector flux linearization.A two-order precision for physical-time step is achieved.Taking low speed flows as examples,the flow over a circular cylinder and the dynamic stall of the NACA0015 airfoil with identical pitching rate are simulated.Computed results agree with published results.It shows that the method simulates unsteady flows at arbitrary Mach number well.

The design of observers for a class of discrete chaotic systems is discussed.Only using a state variable and its time delays,one can construct a control law to implement the synchronization between the investigated chaotic systems and their observers.Simulation results on several well-known chaotic systems show the usefulness of the suggested method.