Designing airfoils according to given pressure (or velocity) distribution is one kind of free boundary problems. Free boundary condition can be coupled with the flow governing equations by variable-domain variational ...Designing airfoils according to given pressure (or velocity) distribution is one kind of free boundary problems. Free boundary condition can be coupled with the flow governing equations by variable-domain variational calculus, which makes it possible to calculate simultaneously the flow field and the free boundary. An accurate deduction of the variable-domain variational principles is taken herein to design airfoils in compressible and incompressible flows. Furthermore, two grid types (H and O) are used in the calculation with better results for the O-type grid. It is shown that convergence is accelerated and good results can be obtained even if the initial guessed airfoil shape is a triangle, demonstrating the strong adaptability of this method.展开更多
In this article a variable-domain variational approach to the entitled problem is presented.A pair of comple- mentary variational principles with a variable domain in terms of temperature and heat-streamfunction are f...In this article a variable-domain variational approach to the entitled problem is presented.A pair of comple- mentary variational principles with a variable domain in terms of temperature and heat-streamfunction are first established.Based on them,two methods of solution—generalized Ritz method and variable-domain FEM— both capable of handling problems with unknown boundaries,are suggested.Then,three sample numerical examples have been tested.The computational process is quite stable,and the results are encouraging.This variational approach can be extended straightforwardly to 3-D inverse problems as well as to other problems in mathematical physics.展开更多
文摘Designing airfoils according to given pressure (or velocity) distribution is one kind of free boundary problems. Free boundary condition can be coupled with the flow governing equations by variable-domain variational calculus, which makes it possible to calculate simultaneously the flow field and the free boundary. An accurate deduction of the variable-domain variational principles is taken herein to design airfoils in compressible and incompressible flows. Furthermore, two grid types (H and O) are used in the calculation with better results for the O-type grid. It is shown that convergence is accelerated and good results can be obtained even if the initial guessed airfoil shape is a triangle, demonstrating the strong adaptability of this method.
文摘In this article a variable-domain variational approach to the entitled problem is presented.A pair of comple- mentary variational principles with a variable domain in terms of temperature and heat-streamfunction are first established.Based on them,two methods of solution—generalized Ritz method and variable-domain FEM— both capable of handling problems with unknown boundaries,are suggested.Then,three sample numerical examples have been tested.The computational process is quite stable,and the results are encouraging.This variational approach can be extended straightforwardly to 3-D inverse problems as well as to other problems in mathematical physics.
