Related papers: Semi-Analytic Solutions to the Noh Problem with a …
The Noh verification test problem is extended beyond the commonly studied ideal gamma-law gas to more realistic equations of state (EOSs) including the stiff gas, the Noble-Abel gas, and the Carnahan-Starling EOS for hard-sphere fluids.…
Relativistic temperature of gas raises the issue of the equation of state (EoS) in relativistic hydrodynamics. We study the EoS for numerical relativistic hydrodynamics, and propose a new EoS that is simple and yet approximates very closely…
We propose a means for constructing highly accurate equations of state (EOS) for elemental solids and liquids essentially from first principles, based upon a particular decomposition of the underlying condensed matter Hamiltonian for the…
We present a systematic approach to construct complete equations of state (EOSs), or to ensure thermodynamic consistency of complete and incomplete forms of EOSs using a minimal and sufficient set of relations. We apply the proposed…
Numerical investigations of partial differential equations with hysteresis have largely focused on simulations, leaving numerical error analysis unexplored and relying mainly on derivative-free nonlinear solvers. This work establishes…
Benchmarking is essential for testing new numerical analysis codes. Their solution is crucial both for testing the partial differential equation solvers and both for the optimization methods. Especially, nature-inspired optimization…
We provide a methodology to obtain black hole (BH) solutions in Ho\v{r}ava gravity (HG) and Einstein Aether (AE) theory for the spherically symmetric (SS) case with a static aether. This methodology consists of first specifying the form of…
A common problem, arising in many different applied contexts, consists in estimating the number of exponentially damped sinusoids whose weighted sum best fits a finite set of noisy data and in estimating their parameters. Many different…
In this work we present a detailed explanation of the construction of an appropriate equation of state (EoS) for nuclear astrophysics. We use a relativistic model in order to obtain an EoS for neutrally charged matter that extends from very…
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…
In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting…
Solution of the Cox-Thompson inverse scattering problem at fixed energy [1,2,3] is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are…
We use a connection between relativistic hydrodynamics and scalar field theory to generate exact analytic solutions describing non-stationary inhomogeneous flows of the perfect fluid with one-parametric equation of state (EOS) $p =…
The notion of semi-classical states is first sharpened by clarifying two issues that appear to have been overlooked in the literature. Systems with linear and quadratic constraints are then considered and the group averaging procedure is…
We revisit global existence and decay for small-data solutions of semilinear wave equations on extremal Reissner-Nordstr\"om black hole backgrounds satisfying the classical null condition, a problem which was previously addressed by the…
Numerical analysis for the stochastic Stokes equations is still challenging even though it has been well done for the corresponding deterministic equations. In particular, the pre-existing error estimates of finite element methods for the…
The equation of state (EOS) is an important issue in numerical simulation codes for relativistic hydrodynamics. We describe a code for adiabatic flows, employing an EOS which is simple and yet approximates very closely the EOS of perfect…
We consider the numerical solution of high-frequency scattering problems modeled by the Helmholtz equation with a bounded obstacle. Although the analysis of this problem dates back at least 50 years, over the past decade or so, tools and…
The thermal properties of black holes in the presence of quantum fields can be revealed through solutions of the semi-classical Einstein equation. We present a brief but self-contained review of the main features of the semi-classical back…
An analytical linear solution of the fully compressible Euler equations is found, in the particular case of a stationary two dimensional flow that passes over an orographic feature with small height-width ratio. A method based on the…