On simplifying assumptions of Runge-Kutta methods for index 2 differential algebraic problems

Computing ◽  
1995 ◽  
Vol 54 (2) ◽  
pp. 185-190 ◽  
Author(s):  
I. Higueras
Keyword(s):  
Simplifying Assumptions ◽  
Index 2 ◽  
Runge Kutta

Reversible methods of Runge-Kutta type for Index-2 DAEs

2004 ◽  
Vol 97 (3) ◽  
pp. 427-440
Author(s):  
R.P.K. Chan ◽  
P. Chartier ◽  
A. Murua
Keyword(s):  
Index 2 ◽  
Runge Kutta

scholarly journals A Comparative Study of Rosenbrock-Type and Implicit Runge-Kutta Time Integration for Discontinuous Galerkin Method for Unsteady 3D Compressible Navier-Stokes equations

2016 ◽  
Vol 20 (4) ◽  
pp. 1016-1044 ◽  
Author(s):  
Xiaodong Liu ◽  
Yidong Xia ◽  
Hong Luo ◽  
Lijun Xuan
Keyword(s):  
Comparative Study ◽  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Time Integration ◽  
Differential Algebraic Equations ◽  
Navier Stokes ◽  
Third Order ◽  
Navier Stokes Equations ◽  
Index 2 ◽  
Runge Kutta

AbstractA comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flows to DNS of turbulent flows, are presented to assess the performance of these schemes. Numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.

scholarly journals Convergence of Lobatto-type Runge–Kutta methods for partitioned differential-algebraic systems of index 2

2021 ◽  
Author(s):  
Rodrigo T. Sato Martín de Almagro
Keyword(s):  
Numerical Scheme ◽  
Algebraic Systems ◽  
Index 2 ◽  
Runge Kutta

AbstractIn this paper a numerical scheme for partitioned systems of index 2 DAEs, such as those arising from nonholonomic mechanical problems, is proposed and its order for a certain class of Runge–Kutta methods we call of Lobatto-type is proven.

Runge-Kutta Pairs of Orders 5(4) using the Minimal Set of Simplifying Assumptions

2009 ◽  
Author(s):  
Ch. Tsitouras ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Minimal Set ◽  
Simplifying Assumptions ◽  
Runge Kutta
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