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On Error-Based Step Size Control for Discontinuous Galerkin Methods for Compressible Fluid Dynamics
We study a temporal step size control of explicit Runge-Kutta (RK) methods for compressible computational fluid dynamics (CFD), including the...
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A Semi-Implicit Numerical Method for Differentially Rotating Compressible Flows
AbstractIn astrophysical fluid dynamics, some types of flows, like e.g., magnetorotational supernova explosions, deal with a highly variable Mach...
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Stability and Time-Step Constraints of Implicit-Explicit Runge-Kutta Methods for the Linearized Korteweg-de Vries Equation
This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries (KdV) equation, using...
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Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics
We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and...
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Using a Low Dissipation Lax–Friedrichs Scheme for Numerical Modeling of Relativistic Flows
AbstractThe Lax–Friedrichs scheme is traditionally considered an alternative to the Godunov scheme, since it does not require solving the Riemann...
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Numerical Features of CESE Schemes
In this chapter, some remarks are made on the numerical characteristics of the CESE schemes described in foregoing chapters. Due to the special...
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Hydrodynamic Modeling of Laser-Induced Shock Waves in Aluminum in a Cylindrically Symmetric Statement
AbstractUsing two-dimensional cylindrically symmetric physical and mathematical model and an algorithm, a numerical investigation of the problem of...
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Dissipative and Dispersive Properties of Finite Difference Schemes for the Linear Transport Equation on A 4 × 3 Metatemplate
AbstractThis article is devoted to the presentation of a new information resource on the Internet: a knowledge base on the dissipative and dispersive...
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Stability and Convergence Analysis of ERKN Integrators for Second-Order ODEs with Highly Oscillatory Solutions
In this chapter, we commence the nonlinear stability and convergence analysis of ERKN integrators for second-order ODEs with highly oscillatory...
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Boundary effects on wave trains in the Exner model of sedimental transport
In this work we compute the numerical solution of the Exner model of sedimentation when a train of waves is imposed at the inflow boundary (E. Macca...
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Interpolatory Conservative-Characteristic Scheme with Improved Dispersion Properties for Computational Fluid Dynamics
AbstractConservative-characteristic schemes for the numerical solution of systems of hyperbolic equations combine the advantages of shock-capturing...
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A dispersion analysis of uniformly high order, interior and boundaries, mimetic finite difference solutions of wave propagation problems
A preliminary stability and dispersion study for wave propagation problems is developed for mimetic finite difference discretizations. The...
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CESE Schemes with Numerical Dissipation
As depicted in Chap. 2 , the interface between the two sub-CEs (CD in Fig. 2.7...
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More Continuous Mass-Lumped Triangular Finite Elements
When solving the wave equation with finite elements, mass lum** allows for explicit time step**, avoiding the cost of a lower-upper decomposition...
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Magnetorotational Supernova Explosions: Jets and Mirror Symmetry Violation
AbstractMagnetorotational processes can significantly affect the dynamics of core-collapse supernovae, resulting to magnetically driven jet-like...
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Enhancing the Convergence of the Multigrid-Reduction-in-Time Method for the Euler and Navier–Stokes Equations
Excessive spatial parallelization can introduce a performance bottleneck due to the communication overhead. While time-parallel method...
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Unmapped Tent Pitching Schemes by Waveform Relaxation
The mapped tent pitching algorithm (MTP) is a very advanced domain decomposition strategy for the parallel solution of hyperbolic problems.
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Hybrid HWENO Method for Nonlinear Degenerate Parabolic Equations
In this paper, a hybrid Hermite weighted essentially non-oscillatory scheme is proposed for nonlinear degenerate parabolic equations which may...
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An efficient three-level weighted essentially non-oscillatory scheme for hyperbolic equations
An improved version of the three-level order-adaptive weighted essentially non-oscillatory (WENO-OA) scheme introduced in Neelan et al. (Results Appl...
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A droplet in a ferrofluid droplet under a rotating magnetic field
Two-dimensional (2-D) direct numerical simulations of a compound droplet (a non-magnetizable droplet wrapped in a ferrofluid droplet) suspended in a...
