• Nuclear Engineering and Technology
• /
• v.55 no.4
• /
• pp.1428-1438
• /
• 2023

A novel Fission Diffusion Synthetic Acceleration (FDSA) method is developed and implemented as a part of a hybrid neutronics method for source convergence acceleration and variance reduction in Monte Carlo (MC) criticality calculations. The acceleration of the MC calculation stems from constructing a synthetic operator and solving a low-order problem using information obtained from previous MC calculations. By applying the P₁ approximation, two correction terms, one for the scalar flux and the other for the current, can be solved in the low-order problem and applied to the transport solution. A variety of one-dimensional (1-D) and two-dimensional (2-D) numerical tests are constructed to demonstrate the performance of FDSA in comparison with the standalone MC method and the coupled MC and Coarse Mesh Finite Difference (MC-CMFD) method on both intended purposes. The comparison results show that the acceleration by a factor of 3-10 can be expected for source convergence and the reduction in MC variance is comparable to CMFD in both slab and full core geometries, although the effectiveness of such hybrid methods is limited to systems with small dominance ratios.

• Journal of Energy Engineering
• /
• v.17 no.4
• /
• pp.233-240
• /
• 2008

Conventionally, the second-order self-adjoint neutron transport equations have been studied using the even parity and the odd parity equations. Recently, however, the SAAF(self-adjoint angular flux) form of neutron transport equation has been introduced as a new option for the second-order self-adjoint equations. In this paper we validated the SAAF equation mathematically and clarified how it relates with the existing even and odd parity equations. We also developed a second-order SAAF differencing formula including DSA(diffusion synthetic acceleration) from the first-order difference equations. Numerical result is attached to show that the proposed methods increases accuracy with effective computational effort.

• Journal of The Korean Astronomical Society
• /
• v.37 no.5
• /
• pp.405-412
• /
• 2004

Cosmological shocks form as an inevitable consequence of gravitational collapse during the large scale structure formation and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration (DSA). We have calculated the evolution of CR modified shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of DSA in 1D quasi-parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc $\ge$ 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that $10^{-4} - 10^{-3}$ of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The CR acceleration efficiency increases with shock Mach number, but it asymptotes to ${\~}50\%$ in high Mach number shocks, regardless of the injection rate and upstream CR pressure. On the other hand, in moderate strength shocks ($M_s {\le} 5$), the pre-existing CRs increase the overall CR energy. We conclude that the CR acceleration at cosmological shocks is efficient enough to lead to significant nonlinear modifications to the shock structures.

• Proceedings of the Korea Concrete Institute Conference
• /
• 2005.05b
• /
• pp.257-260
• /
• 2005

A general electric acceleration testing method for estimation of chloride diffusion coefficient is RCPT and CTH. Also, this testing methods have merit that reduce the testing time. In this paper, an experimental study is executed to investigate the effect of testing method on coefficient of chloride diffusion and it is compared with RCPT and CTH. According to this experiment results, W/C ratio and testing method influence chloride diffusion coefficient of concrete. As W/C ratio is increased, diffusion coefficient in concrete is also increased. Diffusion coefficient obtained by each testing method show the different values. However, there is no remarkable difference between the two testing method.

• Proceedings of the Korean Nuclear Society Conference
• /
• 1995.10a
• /
• pp.103-108
• /
• 1995

By applying the P$_1$ and P$_2$ equations to the operator form of a synthetic acceleration, we derive the p,-acceleration (diffusion synthetic acceleration: DSA) and P$_2$-acceleration (p$_2$SA) schemes in one dimensional slab geometry. We Fourier-analyze the derived acceleration schemes with the discrete-ordinates transport equation and showed that the DSA outperforms the P$_2$SA. These results confirm that one cannot simply assume that replacement of the DSA with a higher order approximation will lead to a better acceleration performance.

• Journal of The Korean Astronomical Society
• /
• v.34 no.4
• /
• pp.293-295
• /
• 2001

A numerical scheme that incorporates a self-consistent cosmic-ray (CR, hereafter) injection model into the combined gas dynamics and CR diffusion-convection code has been developed. The hydro/CR code can follow in a very cos-effective way the evolution of CR modified shocks by adopting subzone shock-tracking and multi-level Adaptive Mesh Refinement techniques. The injection model is based on interactions of the suprathermal particles with self-generated MHD waves in quasi-parallel shocks. The particle injection is followed numerically by filtering the diffusive flux of suprathermal particles across the shock to upstream region according to a velocity-dependent transparency function, which represents the fraction of leaking suprathermal particles. In the strong shock limit of Mach numbers $\ge$20, significant physical processes such as the injection and acceleration seem to become independent of M, while they are sensitively dependent on M for M < 10. Although some particles injected early in the evolution continue to be accelerated to higher energies, the postshock CR pressure reaches a time asymptotic value due to balance between acceleration and diffusion of the CR particles.

• Journal of The Korean Astronomical Society
• /
• v.37 no.4
• /
• pp.225-232
• /
• 2004

Shocks are ubiquitous in astrophysical environments and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration. It is believed that the CR pressure is important in the evolution of the interstellar medium of our galaxy and most of galactic CRs with energies up to ${\~}\;10^{15}$ eV are accelerated by supernova remnant shocks. In this contribution we have studied the CR acceleration at shocks through numerical simulation of 1D, quasi-parallel shocks for a wide range of shock Mach numbers and shock speeds. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies, and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that $10^{-4} - 10^{-3}$ of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number, and high Mach number shocks all evolve towards efficiencies ${\~}50\%$, regardless of the injection rate and upstream CR pressure. We conclude that the injection rates in strong quasi-parallel shocks are sufficient to lead to significant nonlinear modifications to the shock structures, implying the importance of the CR acceleration at astrophysical shocks.

• Nuclear Engineering and Technology
• /
• v.52 no.3
• /
• pp.485-498
• /
• 2020

A diffusion synthetic acceleration (DSA) technique for the S_N transport equation discretized with the linear discontinuous expansion method with subcell balance (LDEM-SCB) on unstructured tetrahedral meshes is presented. The LDEM-SCB scheme solves the transport equation with the discrete ordinates method by using the subcell balances and linear discontinuous expansion of the flux. Discretized DSA equations are derived by consistently discretizing the continuous diffusion equation with the LDEM-SCB method, however, the discretized diffusion equations are not fully consistent with the discretized transport equations. In addition, a fine mesh rebalance (FMR) method is devised to accelerate the discretized diffusion equation coupled with the preconditioned conjugate gradient (CG) method. The DSA method is applied to various test problems to show its effectiveness in speeding up the iterative convergence of the transport equation. The results show that the DSA method gives small spectral radii for the tetrahedral meshes having various minimum aspect ratios even in highly scattering dominant mediums for the homogeneous test problems. The numerical tests for the homogeneous and heterogeneous problems show that DSA with FMR (with preconditioned CG) gives significantly higher speedups and robustness than the one with the Gauss-Seidel-like iteration.

• Journal of The Korean Astronomical Society
• /
• v.39 no.4
• /
• pp.95-105
• /
• 2006

We have calculated the cosmic ray(CR) acceleration at young remnants from Type Ia supernovae expanding into a uniform interstellar medium(ISM). Adopting quasi-parallel magnetic fields, gasdynamic equations and the diffusion convection equation for the particle distribution function are solved in a comoving spherical grid which expands with the shock. Bohm-type diffusion due to self-excited $Alfv\acute{e}n$ waves, drift and dissipation of these waves in the precursor and thermal leakage injection were included. With magnetic fields amplified by the CR streaming instability, the particle energy can reach up to $10^{16}Z$ eV at young supernova remnants(SNRs) of several thousand years old. The fraction of the explosion energy transferred to the CR component asymptotes to 40-50 % by that time. For a typical SNR in a warm ISM, the accelerated CR energy spectrum should exhibit a concave curvature with the power-law slope flattening from 2 to 1.6 at $E{\gtrsim}0.1$ TeV.

• Nuclear Engineering and Technology
• /
• v.49 no.6
• /
• pp.1143-1156
• /
• 2017

This paper describes recent development activities of the GENESIS code, which is a transport code for heterogeneous three-dimensional geometry, focusing on applications to reactor core analysis. For the treatment of anisotropic scattering, the concept of the simplified Pn method is introduced in order to reduce storage of flux moments. The accuracy of the present method is verified through a benchmark problem. Next, the iteration stability of the GENESIS code for the highly voided condition, which would appear in a severe accident (e.g., design extension) conditions, is discussed. The efficiencies of the coarse mesh finite difference and generalized coarse mesh rebalance acceleration methods are verified with various stabilization techniques. Use of the effective diffusion coefficient and the artificial grid diffusion coefficients are found to be effective to stabilize the acceleration calculation in highly voided conditions.