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A Shock Stabilization of the HLLC Riemann Solver for the Carbuncle Instability
The HLLC approximate Riemann solver improves upon the HLL Riemann solver by resolving contact discontinuities. This is a particularly desirable...
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Multidimensional Generalized Riemann Problem Solver for Maxwell’s Equations
Approximate multidimensional Riemann solvers are essential building blocks in designing globally constraint-preserving finite volume time domain and...
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Nonclassical Riemann solver with prescribed kinetics—The hyperbolic regime
This chapter serves as an example of how a kinetic relation can be used to implement Lax’s shock inequalities. Specifically, we consider a model from...
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Finding an Approximate Riemann Solver via Relaxation: Concept and Advantages
We first explain the general concept of relaxation models using the **-**n model for scalar conservation laws. Then we consider the Suliciu model...
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Efficient non-iterative multi-point method for solving the Riemann problem
In computational fluid dynamics (CFD), the Riemann problem is vital for precise fluid flow calculations as it involves the accurate computation of...
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Nonclassical Riemann solver with prescribed kinetics—The hyperbolic-elliptic regime
This chapter deals with a hyperbolic-elliptic model of phase transition dynamics. The model is a typical p-system, where the stress can be decreased...
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High-order accurate solutions of generalized Riemann problems of nonlinear hyperbolic balance laws
We provide a systematic study for the generalized Riemann problem (GRP) of the nonlinear hyperbolic balance law, which is critically concerned with...
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Application of Hybrid Riemann Solvers Based on HLLC and HLL for Simulation of Flows with Gas-Dynamic Discontinuities
AbstractThe application of hybrid approximate Riemann solvers based on standard HLLC and HLL solvers is discussed. Three different hybrid solvers are...
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Development and Validation of a Riemann Solver in OpenFOAM for Non-ideal Compressible Fluid Dynamics
Recently, there is an increased interest in supercritical CO \(_2\) and...
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An Hybrid Solver to Compute a Turbulent Compressible Model
In this paper, we propose a numerical strategy to compute a turbulence model for compressible flows, including a dynamic estimation of the jump in...
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Dual-solver research based on the coupling of flux reconstruction and finite volume methods
Accurate simulation of vortex-dominated flows has been an important issue for numerical methods in computational fluid dynamics. The recently...
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A Review of Riemann Solvers for Hypersonic Flows
In the design of the hypersonic airliner which can greatly shorten the flight time and conduct space travel, it is of great significance for a...
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Convergence of a Generalized Riemann Problem Scheme for the Burgers Equation
In this paper, we study the convergence of a second-order finite volume approximation of the scalar conservation law. This scheme is based on the...
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Using Piecewise Parabolic Reconstruction of Physical Variables in the Rusanov Solver. I. The Special Relativistic Hydrodynamics Equations
AbstractThe Rusanov solver for solving hydrodynamic equations is one of the most robust schemes in the class of Riemann solvers. For special...
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Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows
A high-order gas kinetic flux solver (GKFS) is presented for simulating inviscid compressible flows. The weighted essentially non-oscillatory (WENO)...
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Machine Learning Approaches for the Solution of the Riemann Problem in Fluid Dynamics: a Case Study
We present our results by using a machine learning (ML) approach for the solution of the Riemann problem for the Euler equations of fluid dynamics....
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Scalar modular bootstrap and zeros of the Riemann zeta function
Using the technology of harmonic analysis, we derive a crossing equation that acts only on the scalar primary operators of any two-dimensional...
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A high-order scheme based on lattice Boltzmann flux solver for viscous compressible flow simulations
In this paper, a high-order scheme based on the lattice Boltzmann flux solver (LBFS) is proposed to simulate viscous compressible flows. The flux...
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Divide-and-Conquer Solver in Tensor-Train Format for d-Dimensional Time-Space Fractional Diffusion Equations
A divide-and-conquer solver coupled with Tensor-Train (TT) format is proposed for solving the d -dimensional time-space fractional diffusion equations...
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An Approximate Riemann Solver for Advection–Diffusion Based on the Generalized Riemann Problem
We construct an approximate Riemann solver for scalar advection–diffusion equations with piecewise polynomial initial data. The objective is to...
