In this paper,we consider high order multi-domain penalty spectral Galerkin methods for the approximation of hyperbolic conservation laws.This formulation has a penalty parameter which can vary in space and time,allow...In this paper,we consider high order multi-domain penalty spectral Galerkin methods for the approximation of hyperbolic conservation laws.This formulation has a penalty parameter which can vary in space and time,allowing for flexibility in the penalty formulation.This flexibility is particularly advantageous for problems with an inhomogeneous mesh.We show that the discontinuous Galerkin method is equivalent to the multi-domain spectral penalty Galerkin method with a particular value of the penalty parameter.The penalty parameter has an effect on both the accuracy and stability of the method.We examine the numerical issues which arise in the implementation of high order multi-domain penalty spectral Galerkin methods.The coefficient truncation method is proposed to prevent the rapid error growth due to round-off errors when high order polynomials are used.Finally,we show that an inconsistent evaluation of the integrals in the penalty method may lead to growth of errors.Numerical examples for linear and nonlinear problems are presented.展开更多
In[J.Comput.Phys.192(1),pp.325-354(2003)],we have developed a multidomain spectral method with stable and conservative penalty interface conditions for the numerical simulation of supersonic reactive recessed cavity f...In[J.Comput.Phys.192(1),pp.325-354(2003)],we have developed a multidomain spectral method with stable and conservative penalty interface conditions for the numerical simulation of supersonic reactive recessed cavity flows with homogeneous grid.In this work,the previously developed methodology is generalized to inhomogeneous grid to simulate the two dimensional supersonic injector-cavity system.Non-physical modes in the solution generated at the domain interfaces due to the spatial grid inhomogeneity are minimized using the new weighted multi-domain spectral penalty method.The proposed method yields accurate and stable solutions of the injector-cavity system which agree well with experiments qualitatively.Through the direct numerical simulation of the injector-cavity system using the weighted method,the geometric effect of the cavity wall on pressure fluctuations is investigated.It is shown that the recessed slanted cavity attenuates pressure fluctuations inside cavity enabling the cavity to act potentially as a stable flameholder for scramjet engine.展开更多
基金The work of both authors has been supported by the NSF under Grant No.DMS-0608844.
文摘In this paper,we consider high order multi-domain penalty spectral Galerkin methods for the approximation of hyperbolic conservation laws.This formulation has a penalty parameter which can vary in space and time,allowing for flexibility in the penalty formulation.This flexibility is particularly advantageous for problems with an inhomogeneous mesh.We show that the discontinuous Galerkin method is equivalent to the multi-domain spectral penalty Galerkin method with a particular value of the penalty parameter.The penalty parameter has an effect on both the accuracy and stability of the method.We examine the numerical issues which arise in the implementation of high order multi-domain penalty spectral Galerkin methods.The coefficient truncation method is proposed to prevent the rapid error growth due to round-off errors when high order polynomials are used.Finally,we show that an inconsistent evaluation of the integrals in the penalty method may lead to growth of errors.Numerical examples for linear and nonlinear problems are presented.
基金The first(WSD)and second authors(DG)gratefully acknowledge the support of this work by the AFOSR under contract number FA9550-08-1-0200 and DOE under contract number DE-FG02-98ER25346The third author(JHJ)has been supported by the NSF under Grant No.DMS-0608844The authors also thank the anonymous referees for their careful reading and helpful suggestions。
文摘In[J.Comput.Phys.192(1),pp.325-354(2003)],we have developed a multidomain spectral method with stable and conservative penalty interface conditions for the numerical simulation of supersonic reactive recessed cavity flows with homogeneous grid.In this work,the previously developed methodology is generalized to inhomogeneous grid to simulate the two dimensional supersonic injector-cavity system.Non-physical modes in the solution generated at the domain interfaces due to the spatial grid inhomogeneity are minimized using the new weighted multi-domain spectral penalty method.The proposed method yields accurate and stable solutions of the injector-cavity system which agree well with experiments qualitatively.Through the direct numerical simulation of the injector-cavity system using the weighted method,the geometric effect of the cavity wall on pressure fluctuations is investigated.It is shown that the recessed slanted cavity attenuates pressure fluctuations inside cavity enabling the cavity to act potentially as a stable flameholder for scramjet engine.
