Radially Symmetrical Problems for Compressible Fluids with a High-Resolution Boundary Condition

Imposing appropriate numerical boundary conditions at the symmetrical center r=0 is vital when computing compressible fluids with radial symmetry.Extrapolation and other traditional techniques are often employed,but spurious numerical oscillations or wall-heating phenomena can occur.In this paper,we emphasize that because of the conservation property,the updating formula of the boundary cell average can coincide with the one for interior cell averages.To achieve second-order accuracy both in time and space,we associate obtaining the inner boundary value at r=0 with the resolution of the corresponding one-sided generalized Riemann problem(GRP).Acoustic approximation is applied in this process.It creates conditions to avoid the singularity of type 1/r and aids in obtaining the value of the singular quantity using L’Hospital’s rule.Several challenging scenarios are tested to demonstrate the effectiveness and robustness of our approach.

Adaptive Multi-Resolution Method for 3D Reactive Flows with Level Set Front Capturing

For compressible reactive flows with stiff source terms,a new block-based adaptive multi-resolution method coupled with the adaptive multi-resolution representation model for ZND detonation and a conservative front capturing method based on a level-set technique is presented.When simulating stiff reactive flows,underresolution in space and time can lead to incorrect propagation speeds of discontinuities,and numerical dissipation makes it impossible for traditional shock-capturing methods to locate the detonation front.To solve these challenges,the proposed method leverages an adaptive multi-resolution representation model to separate the scales of the reaction from those of fluid dynamics,achieving both high-resolution solutions and high efficiency.A level set technique is used to capture the detonation front sharply and reduce errors due to the inaccurate prediction of detonation speed.In order to ensure conservation,a conservative modified finite volume scheme is implemented,and the front transition fluxes are calculated by considering a Riemann problem.A series of numerical examples of stiff detonation simulations are performed to illustrate that the present method can acquire the correct propagation speed and accurately capture the sharp detonation front.Comparative numerical results also validate the approach’s benefits and excellent performance.

A Gas-Kinetic Scheme for Collisional Vlasov-Poisson Equations in Cylindrical Coordinates

Many configurations in plasma physics are axisymmetric,it will be more convenient to depict them in cylindrical coordinates compared with Cartesian coordinates.In this paper,a gas-kinetic scheme for collisional Vlasov-Poisson equations in cylindrical coordinates is proposed,our algorithm is based on Strang splitting.The equation is divided into two parts,one is the kinetic transport-collision part solved by multiscale gas-kinetic scheme,and the other is the acceleration part solved by a Runge-Kutta solver.The asymptotic preserving property of whole algorithm is proved and it’s applied on the study of charge separation problem in plasma edge and 1D Z-pinch configuration.Numerical results show it can capture the process fromnon-equilibrium to equilibrium state by Coulomb collisions,and numerical accuracy is obtained.