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Highlights • An efficient time-marching procedure is proposed for nonlinear parabolic models. • The method is adaptive and entirely automated, requiring no expertise from the user. • It is locally defined, introducing modified elements to guarantee stability. • The modified formulation reproduces the analytical solution for SDOF models. • It enables reduced solver efforts and it stands as a non-iterative single-step procedure. Abstract This work proposes a locally stabilized, forward Euler method for time domain analyses, which performs considering the relation between the adopted temporal and spatial discretizations. Here, the standard expression of the forward Euler method is considered to approximate the time derivative of the unknown variable, and the local (or element) matrices of the spatially discretized model are modified, if the stability criterion of the forward Euler method is not locally fulfilled. Thus, a locally defined, adaptive time marching methodology is provided, which has guaranteed stability, very good accuracy, and is highly versatile and effective. In the new technique, only reduced systems of equations have to be dealt with (in order to ensure stability), and iterative procedures are never required when nonlinear models are considered. Thus, the proposed methodology is very efficient. In addition, the new technique is very simple to implement and entirely automatized, requiring no decision or expertise from the user. Numerical results are presented at the end of the paper, illustrating the performance and effectiveness of the new approach. [ABSTRACT FROM AUTHOR]

Abstract This work proposes a locally stabilized central difference method for time domain analyses, which performs considering the relation between the adopted temporal and spatial discretizations. Here, the standard expressions of the Central Difference Method (CDM) are considered to approximate the time derivatives of the incognita field, and the local (or element) matrices of the spatially discretized model are modified, if the stability criterion of the CDM is not locally fulfilled. Thus, a locally defined time marching methodology is provided, which may be up to fourth order accurate, has guaranteed stability, enhanced precision, and is highly efficient and versatile. The new technique may be stated as a semi-explicit/explicit approach; in this context, just reduced systems of equations have to be dealt with in the analyses and iterative procedures are never required, when nonlinear models are focused. In addition, the new technique is also very simple to implement and entirely automatized, requiring no decision or expertise from the user. Numerical results are presented along the paper, illustrating the performance and effectiveness of the new approach. Highlights • An effective time-marching procedure is proposed for nonlinear dynamics. • It is locally defined, introducing modified elements to guarantee stability. • The method has enhanced accuracy, it is simple and entirely automatized. • It enables reduced solver efforts and it stands as a non-iterative procedure. [ABSTRACT FROM AUTHOR]

Abstract: Solution of governing equations for one-dimensional compressible unsteady flow has been performed traditionally using a homogenously distributed spatial mesh. In the resulting node structure, the internal nodes are solved by applying a shock capturing finite difference numerical method whereas the solution of the end nodes, which define the boundary conditions of the pipe, is undertaken by means of the Method of Characteristics. Besides the independent solution of every method, the coupling between the information obtained by the method of characteristics and the finite difference method is key in order to reach a good accuracy in gas dynamics modeling. The classical spatial mesh could provide numerical problems leading the boundary to generate lack of mass, momentum and energy conservation because of the interpolation methodology usually applied to draw the characteristics and path lines from its departure point at calculation time to the end of the pipe during the next time-step. To deal with this undesirable behavior, in this work a modification of the traditional grid including an extra node close to the boundary is proposed in order to explore its ability to provide numerical results with higher conservation fulfillment. [Copyright &y& Elsevier]