Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/polynomial-chaos-methods-for-hyperbolic-partial-differential-equations-vsazjh3BCN
References (24)
-
A. Harten (1983)
On the symmetric form of systems of conservation laws with entropyJournal of Computational Physics, 49
-
B. Leer (1997)
Towards the Ultimate Conservative Difference SchemeJournal of Computational Physics, 135
-
Vidar Stiernström, M. Almquist, K. Mattsson (2023)
Boundary-optimized summation-by-parts operators for finite difference approximations of second derivatives with variable coefficientsJ. Comput. Phys., 491
-
M. Deb, I. Babuska, J. Oden (2001)
Solution of stochastic partial differential equations using Galerkin finite element techniquesComputer Methods in Applied Mechanics and Engineering, 190
-
Per Pettersson, G. Iaccarino, J. Nordström (2013)
An intrusive hybrid method for discontinuous two-phase flow under uncertaintyComputers & Fluids, 86
-
Per Pettersson, G. Iaccarino, J. Nordström (2009)
Numerical analysis of the Burgers' equation in the presence of uncertaintyJ. Comput. Phys., 228
-
Bkam Leer, B. Leer (1979)
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's methodJournal of Computational Physics, 32
-
M. Gerritsen, P. Olsson (1996)
Designing an efficient solution strategy for fluid flows. 1. A stable high order finite difference scheme and sharp shock resolution for the Euler equationsJournal of Computational Physics, 129
-
B. Strand (1994)
Summation by parts for finite difference approximations for d/dxJournal of Computational Physics, 110
-
Heng Li, Dongxiao Zhang (2009)
Efficient and Accurate Quantification of Uncertainty for Multiphase Flow With the Probabilistic Collocation MethodSpe Journal, 14
-
S. Gottlieb, Chi-Wang Shu (1998)
Total variation diminishing Runge-Kutta schemesMath. Comput., 67
-
Qian Chen, D. Gottlieb, J. Hesthaven (2005)
Uncertainty analysis for the steady-state flows in a dual throat nozzleJournal of Computational Physics, 204
-
M. Carpenter, J. Nordström, D. Gottlieb (1999)
A Stable and Conservative Interface Treatment of Arbitrary Spatial AccuracyJournal of Computational Physics, 148
-
B. Debusschere, H. Najm, P. Pébay, O. Knio, R. Ghanem, O. Maître (2005)
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic ProcessesSIAM J. Sci. Comput., 26
-
C. Schwab, S. Tokareva (2013)
High order approximation of probabilistic shock profiles in hyperbolic conservation laws with uncertain initial dataMathematical Modelling and Numerical Analysis, 47
-
D. Xiu, G. Karniadakis (2002)
The Wiener-Askey Polynomial Chaos for Stochastic Differential EquationsSIAM J. Sci. Comput., 24
-
H. Kreiss, G. Scherer (1974)
Finite Element and Finite Difference Methods for Hyperbolic Partial Differential Equations -
Sofia Eriksson, Q. Abbas, J. Nordström (2011)
A stable and conservative method for locally adapting the design order of finite difference schemesJ. Comput. Phys., 230
-
Q. Abbas, E. Weide, J. Nordström (2009)
Accurate and stable calculations involving shocks using a new hybrid scheme -
Mike Chen, A. Keller, Zhen Lu, D. Zhang, G. Zyvoloski (2008)
Uncertainty Quantification for Multiphase Flow in Random Porous Media Using KL-Based Moment Equation Approaches -
C. Pettit, P. Beran (2006)
Spectral and multiresolution Wiener expansions of oscillatory stochastic processesJournal of Sound and Vibration, 294
-
J. Haas, B. Sturtevant (1987)
Interaction of weak shock waves with cylindrical and spherical gas inhomogeneitiesJournal of Fluid Mechanics, 181
-
A. Harten, P. Lax, B. Leer (1983)
On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation LawsSiam Review, 25
-
G. Sod (1978)
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation lawsJournal of Computational Physics, 27
- Publisher
- Springer International Publishing
- Copyright
- © Springer International Publishing Switzerland 2015
- ISBN
- 978-3-319-10713-4
- Pages
- 149 –172
- DOI
- 10.1007/978-3-319-10714-1_9
- Publisher site
- See Chapter on Publisher Site
Abstract
[In this chapter, we investigate a two-phase flow generalization of the Euler equations. A symmetrized problem formulation that generalizes previous energy estimates in for the Euler equations is used for the stochastic Galerkin system. The solution is expected to develop non-smooth features that are localized in space. Consequently, we adapt the numerical method to the smoothness of the solution. Finite-difference operators in summation-by-parts (SBP) form are used for the high-order spatial discretization, and the HLL-flux and MUSCL reconstruction are employed for shock-capturing in the non-smooth region. The coupling between the different solution regions is performed with a weak imposition of the interface conditions through an interface using a penalty technique.]
Published: Sep 17, 2014
Keywords: Euler Equation; Hybrid Scheme; Deterministic Problem; Stochastic Mode; Stochastic Collocation