Nielsen, Entropy stable discontinuous interfaces coupling for the three-dimensional compressible Navier-Stokes equations, J. Nielsen, Entropy stable staggered grid discontinuous spectral collocation methods of any order for the compressible Navier-Stokes equations, SIAM J.
Ranocha, Analysis of artificial dissipation of explicit and implicit time-integration methods, Int. Hillstrom, User Guide for MINPACK-1, Technical report ANL-80-74, Argonne National Laboratory, Argonne, Illinois, 1980. Lozano, Entropy production by explicit Runge-Kutta schemes, J. Rohde, Fully discrete, entropy conservative schemes of arbitrary order, SIAM J. Calvo, Numerical methods for non conservative perturbations of conservative problems, Comput. Kojima, Invariants preserving schemes based on explicit Runge-Kutta methods, BIT, 56 ( 2016 ), pp. Karpeev, Mesh algorithms for PDE with Sieve I: Mesh distribution, Sci. Ketcheson and Relaxation : Conservation and stability for inner-product norms, SIAM J. Ketcheson, Highly efficient strong stability-preserving Runge-Kutta methods with low-storage implementations, SIAM J. , SciPy: Open Source Scientific Tools for Python, 2001. Higueras and Monotonicity : Inner product norms, J. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, Springer Ser. Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Springer Ser. Quispel, Geometric integration methods that preserve Lyapunov functions, BIT, 45 ( 2005 ), pp. Shu, Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations, World Scientific, Singapore, 2011. Carpenter, Entropy stable space-time discontinuous Galerkin schemes with summation-by-parts property for hyperbolic conservation laws, J. Parsani, Entropy stable $p$-nonconforming discretizations with the summation-by-parts property for the compressible Navier-Stokes equations, Comput. Parsani, Entropy stable $p$-nonconforming discretizations with the summation-by-parts property for the compressible Euler equations, SIAM J. Mastroserio, Explicit methods based on a class of four stage fourth order Runge-Kutta methods for preserving quadratic laws, J. Verwer, Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations, CWI Monogr. Parsani, Conservative and entropy stable solid wall boundary conditions for the compressible Navier-Stokes equations: Adiabatic wall and heat entropy transfer, J. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag, Berlin, 2010. Fisher, Towards an entropy stable spectral element framework for computational fluid dynamics, in Proceedings of the 54th AIAA Aerospace Sciences Meeting, AIAA 2016-1058, American Institute of Aeronautics and Astronautics, 2016. Kennedy, Fourth-Order 2N Runge-Kutta Schemes, Technical report NASA-TM-109112, NASA, 1994. Frankel, Entropy stable spectral collocation schemes for the Navier-Stokes equations: Discontinuous interfaces, SIAM J. Rández, Runge-Kutta projection methods with low dispersion and dissipation errors, Adv. Rández, Projection methods preserving Lyapunov functions, BIT, 50 ( 2010 ), pp. Rández, On the preservation of invariants by explicit Runge-Kutta methods, SIAM J. Butcher, Numerical Methods for Ordinary Differential Equations, John Wiley & Sons, Chichester, 2008. , Prentice-Hall, Englewood Cliffs, NJ, 1973. Brent, Algorithms for Minimization Without Derivatives, Ser. Shampine, An efficient Runge-Kutta (4, 5) pair, Comput. Shampine, A 3 (2) pair of Runge-Kutta formulas, Appl. Zhang, PETSc Users Manual, Technical report ANL-95/11 (revision 3.10), Argonne National Laboratory, 2018. Zhang, PETSc/TS: A Modern Scalable ODE/DAE Solver Library,, 2018. The effectiveness of this approach is proved analytically and demonstrated in several numerical examples, including applications to high order entropy-conservative and entropy-stable semidiscretizations on unstructured grids for the compressible Euler and Navier-Stokes equations.ġ. The computational cost at each step is the solution of one additional scalar algebraic equation for which a good initial guess is available. The technique can be applied to both explicit and implicit Runge-Kutta methods and requires only a small modification to existing implementations.
Moreover, other desirable stability (such as strong stability preservation) and efficiency (such as low storage requirements) properties are preserved.
#MODEL BUILDER SPATIAL ANALYST FAILS ON PYTHON EXPORT UPDATE#
Conservation, dissipation, or other solution properties with respect to any convex functional are enforced by the addition of a relaxation parameter that multiplies the Runge-Kutta update at each step. The framework of inner product norm preserving relaxation Runge-Kutta methods is extended to general convex quantities.
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