Related papers: An approach to the Riemann problem for SPH invisci…
The solutions for a Riemann problem arising in chemical flooding models are studied using vanishing viscosity as an admissibility criterion. We show that when the flow function depends non-monotonically on the concentration of chemicals,…
We compare high-order methods including spectral difference (SD), flux reconstruction (FR), the entropy-stable discontinuous Galerkin spectral element method (ES-DGSEM), modal discontinuous Galerkin methods, and WENO to select the best…
The Finite Volume Method in Computational Fluid Dynamics to numerically model a fluid flow problem involves the process of formulating the numerical flux at the faces of the control volume. This process is important in deciding the…
In this paper, we study the isothermal gas dynamics. We first establish the global existence of strong solutions to the one-dimensional isothermal Navier-Stokes system for smooth initial data without any smallness conditions, assuming that…
We present and test a new, special-relativistic formulation of Smoothed Particle Hydrodynamics (SPH). Our approach benefits from several improvements with respect to earlier relativistic SPH formulations. It is self-consistently derived…
Zero viscosity limits are central to the study of classical shock waves. By identifying the correct physical (Lax admissible) shocks, they are a cornerstone in the design of analytical and numerical schemes. For relativistic fluid flow,…
An exact discontinuity capturing central solver developed recently, named MOVERS (Method of Optimal Viscosity for Enhanced Resolution of Shocks, J Computat Phys 2009;228:770-798), is analyzed and improved further to make it entropy stable.…
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…
We consider a sharp-interface approach for the inviscid isothermal dynamics of compressible two-phase flow, that accounts for phase transition and surface tension effects. To fix the mass exchange and entropy dissipation rate across the…
We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary…
We present a new hydrodynamic scheme named Godunov Density-Independent Smoothed Particle Hydrodynamics (GDISPH), that can accurately handle shock waves and contact discontinuities without any manually tuned parameters. This is in contrast…
This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of…
The smoothed particle hydrodynamics (SPH) method is a useful numerical tool for the study of a variety of astrophysical and planetlogical problems. However, it turned out that the standard SPH algorithm has problems in dealing with…
We consider the Riemann problem composed of two shocks for the 1D Euler system. We show that the Riemann solution with two shocks is stable and unique in the class of weak inviscid limits of solutions to the Navier-Stokes equations with…
We develop, and implement in a Finite Volume environment, a density-based approach for the Euler equations written in conservative form using density, momentum, and total energy as variables. Under simplifying assumptions, these equations…
Shock waves in high-speed fluid dynamics produce near-discontinuities in the fluid momentum, density, and energy. Most contemporary works use artificial viscosity or limiters as numerical mitigation of the Gibbs--Runge oscillations that…
In this work, a localized artificial-viscosity/diffusivity method is proposed for accurately capturing discontinuities in compressible flows. There have been numerous efforts to improve the artificial diffusivity formulation in the last two…
We present new methods to solve the Riemann problem both exactly and approximately for general equations of state (EoS) to facilitate realistic modeling and understanding of astrophysical flows. The existence and uniqueness of the new exact…
Godunov-type methods, which obtain numerical fluxes through local Riemann problems at cell interfaces, are among the most fundamental and widely used numerical methods in computational fluid dynamics. Exact Riemann solvers faithfully solve…
An extended immersed boundary method utilizing a semi-implicit direct forcing approach for the simulation of confined incompressible viscous thermal flow problems is presented. The method utilizes a Schur complement approach to enforce the…