Related papers: Improving the quantification of overshooting shock…
This note introduces a simple metric for benchmarking shock-capturing schemes. This metric is especially focused on the shock-capturing overshoots, which may undermine the robustness of numerical simulations, as well as the reliability of…
We provide a `user guide' to the literature of the past twenty years concerning the modeling and approximation of discontinuous solutions to nonlinear hyperbolic systems that admit small-scale dependent shock waves. We cover several classes…
In this paper, continuous research is undertaken to explore the underlying mechanism of numerical shock instabilities of Godunov-type schemes for strong shocks. By conducting dissipation analysis of Godunov-type schemes and a sequence of…
For a model of nonlinear elastodynamics, we construct a finite volume scheme which is able to capture nonclassical shocks (also called undercompressive shocks). Those shocks verify an entropy inequality but are not admissible in the sense…
A series of third- and fifth-order hybrid compact least-squares central weighted essentially non-oscillatory schemes are proposed and applied to curvilinear structured grids for the finite volume method. In smooth regions, compact…
The shock instability problem commonly arises in flow simulations involving strong shocks, particularly when employing high-order schemes, limiting their applications in hypersonic flow simulations. This study focuses on exploring the…
In this work, we propose a novel selective discontinuity sensor approach for numerical simulations of the compressible Navier-Stokes equations. Since transformation to characteristic space is already a common approach to reduce…
We introduce stabilized spline collocation schemes for the numerical solution of nonlinear, hyperbolic conservation laws. A nonlinear, residual-based viscosity stabilization is combined with a projection stabilization-inspired linear…
In this exploratory study, we apply shock-capturing schemes within the framework of the Particles on Demand kinetic model to simulate compressible flows with mild and strong shock waves and discontinuities. The model is based on the…
High-speed turbulent flows are encountered in most space-related applications (including exploration, tourism and defense fields) and represent a subject of growing interest in the last decades. A major challenge in performing high-fidelity…
A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…
Preserving scalar boundedness is important for numerical schemes used in turbulent compressible multi-component flow simulations to prevent unphysical results and unstable simulations. However, ensuring scalar boundedness for high-order,…
Modern shock-capturing schemes often suffer from numerical shock anomalies if the flow field contains strong shocks, which may limit their further application in hypersonic flow computations. In the current study, we devote our efforts to…
Fluid discontinuities, such as shock fronts and vortex sheets, can reflect waves and become unstable to corrugation. Analytical calculations of these phenomena are tractable in the simplest cases only, while their numerical simulations are…
We present a shock capturing method for large-eddy simulation of turbulent flows. The proposed method relies on physical mechanisms to resolve and smooth sharp unresolved flow features that may otherwise lead to numerical instability, such…
The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for…
We study dissipation as a function of sample thickness in solids under global oscillatory shear applied to the top layer of the sample. Two types of damping mechanism are considered: Langevin and Dissipative Particle Dynamics (DPD). In the…
We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…
Simulations of single- and multi-species compressible flows with shock waves and discontinuities are conducted using a weighted compact nonlinear scheme (WCNS) with a newly developed sixth order localized dissipative interpolation. In…
We study the position estimation of a mechanical oscillator undergoing both detuned parametric amplification and continuous quantum measurement. This model, which can be utilised to produce squeezed states, is applied to a general…