High order strong stability preserving time discretizations

S Gottlieb, DI Ketcheson, CW Shu - Journal of Scientific Computing, 2009 - Springer
Strong stability preserving (SSP) high order time discretizations were developed to ensure
nonlinear stability properties necessary in the numerical solution of hyperbolic partial …

[KNJIGA][B] Strong stability preserving Runge-Kutta and multistep time discretizations

S Gottlieb, D Ketcheson, CW Shu - 2011 - World Scientific
Strong Stability Preserving Explicit Runge—Kutta Methods | Strong Stability Preserving
Runge-Kutta and Multistep Time Discretizations World Scientific Search This Book Anywhere …

Highly efficient strong stability-preserving Runge–Kutta methods with low-storage implementations

DI Ketcheson - SIAM Journal on Scientific Computing, 2008 - SIAM
Strong stability-preserving (SSP) Runge–Kutta methods were developed for time integration
of semidiscretizations of partial differential equations. SSP methods preserve stability …

Simulations of pulsating one-dimensional detonations with true fifth order accuracy

AK Henrick, TD Aslam, JM Powers - Journal of Computational Physics, 2006 - Elsevier
A novel, highly accurate numerical scheme based on shock-fitting coupled with fifth order
spatial and temporal discretizations is applied to a classical unsteady detonation problem to …

Explicit higher-order accurate isogeometric collocation methods for structural dynamics

JA Evans, RR Hiemstra, TJR Hughes, A Reali - Computer Methods in …, 2018 - Elsevier
The objective of the present work is to develop efficient, higher-order space-and time-
accurate, methods for structural dynamics. To this end, we present a family of explicit …

Optimal implicit strong stability preserving Runge–Kutta methods

DI Ketcheson, CB Macdonald, S Gottlieb - Applied Numerical Mathematics, 2009 - Elsevier
Strong stability preserving (SSP) time discretizations were developed for use with spatial
discretizations of partial differential equations that are strongly stable under forward Euler …

Embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods

I Fekete, S Conde, JN Shadid - Journal of Computational and Applied …, 2022 - Elsevier
We construct a family of embedded pairs for optimal explicit strong stability preserving
Runge–Kutta methods of order 2≤ p≤ 4 to be used to obtain numerical solution of spatially …

Adjoint sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Adjoint Shadowing (NILSAS)

A Ni, C Talnikar - Journal of Computational Physics, 2019 - Elsevier
We develop the NILSAS algorithm, which performs adjoint sensitivity analysis of chaotic
systems via computing the adjoint shadowing direction. NILSAS constrains its minimization …

High-order shock-fitted detonation propagation in high explosives

CM Romick, TD Aslam - Journal of Computational Physics, 2017 - Elsevier
A highly accurate numerical shock and material interface fitting scheme composed of fifth-
order spatial and third-or fifth-order temporal discretizations is applied to the two …

Unsteady adjoint of pressure loss for a fundamental transonic turbine vane

C Talnikar, Q Wang… - Journal of …, 2017 - asmedigitalcollection.asme.org
High-fidelity simulations, eg, large eddy simulation (LES), are often needed for accurately
predicting pressure losses due to wake mixing and boundary layer development in …