The adaptive generalized Riemann problem(GRP)scheme for 2-D compressible fluid flows has been proposed in[J.Comput.Phys.,229(2010),1448–1466]and it displays the capability in overcoming difficulties such as the start...The adaptive generalized Riemann problem(GRP)scheme for 2-D compressible fluid flows has been proposed in[J.Comput.Phys.,229(2010),1448–1466]and it displays the capability in overcoming difficulties such as the start-up error for a single shock,and the numerical instability of the almost stationary shock.In this paper,we will provide the accuracy study and particularly show the performance in simulating 2-D complex wave configurations formulated with the 2-D Riemann problems for compressible Euler equations.For this purpose,we will first review the GRP scheme briefly when combined with the adaptive moving mesh technique and consider the accuracy of the adaptive GRP scheme via the comparison with the explicit formulae of analytic solutions of planar rarefaction waves,planar shock waves,the collapse problem of a wedge-shaped dam and the spiral formation problem.Then we simulate the full set of wave configurations in the 2-D four-wave Riemann problems for compressible Euler equations[SIAM J.Math.Anal.,21(1990),593–630],including the interactions of strong shocks(shock reflections),vortex-vortex and shock-vortex etc.This study combines the theoretical results with the numerical simulations,and thus demonstrates what Ami Harten observed"for computational scientists there are two kinds of truth:the truth that you prove,and the truth you see when you compute"[J.Sci.Comput.,31(2007),185–193].展开更多
There are great challenges for traditional three-dimensional( 3-D) interferometric inverse synthetic aperture radar( In ISAR) imaging algorithms of ship targets w ith 2-D sparsity in actual radar imaging system. To de...There are great challenges for traditional three-dimensional( 3-D) interferometric inverse synthetic aperture radar( In ISAR) imaging algorithms of ship targets w ith 2-D sparsity in actual radar imaging system. To deal w ith this problem,a novel 3-D In ISAR imaging method is proposed in this paper.First,the high-precision gradient adaptive algorithm w as adopted to reconstruct the echoes in range dimension. Then the method of minimizing the entropy of the average range profile w as applied to estimate the parameters w hich are used to compensate translation components of the received echoes. Besides,the phase adjustment and image coregistration of the sparse echoes w ere achieved at the same time through the approach of the joint phase autofocus. Finally,the 3-D geometry coordinates of the ship target w ith 2-D sparsity w ere reconstructed by combining the range measurement and interferometric processing of the ISAR images. Simulation experiments w ere carried out to verify the practicability and effectiveness of the algorithm in the case that the received echoes are in 2-D sparsity.展开更多
基金supported by the Key Program from Beijing Educational Commission(KZ200910028002)PHR(IHLB)and NSFC(10971142,11031001)+3 种基金supported by the National Basic Research Program under the Grant 2005CB321703the National Natural Science Foundation of China(No.10925101,10828101)the Program for New Century Excellent Talents in University(NCET-07-0022)the Doctoral Program of Education Ministry of China(No.20070001036).
文摘The adaptive generalized Riemann problem(GRP)scheme for 2-D compressible fluid flows has been proposed in[J.Comput.Phys.,229(2010),1448–1466]and it displays the capability in overcoming difficulties such as the start-up error for a single shock,and the numerical instability of the almost stationary shock.In this paper,we will provide the accuracy study and particularly show the performance in simulating 2-D complex wave configurations formulated with the 2-D Riemann problems for compressible Euler equations.For this purpose,we will first review the GRP scheme briefly when combined with the adaptive moving mesh technique and consider the accuracy of the adaptive GRP scheme via the comparison with the explicit formulae of analytic solutions of planar rarefaction waves,planar shock waves,the collapse problem of a wedge-shaped dam and the spiral formation problem.Then we simulate the full set of wave configurations in the 2-D four-wave Riemann problems for compressible Euler equations[SIAM J.Math.Anal.,21(1990),593–630],including the interactions of strong shocks(shock reflections),vortex-vortex and shock-vortex etc.This study combines the theoretical results with the numerical simulations,and thus demonstrates what Ami Harten observed"for computational scientists there are two kinds of truth:the truth that you prove,and the truth you see when you compute"[J.Sci.Comput.,31(2007),185–193].
基金Sponsored by the National Natural Science Foundation of China(Grant Nos.61622107 and 61871146)the Fundamental Research Funds for the Central Universities
文摘There are great challenges for traditional three-dimensional( 3-D) interferometric inverse synthetic aperture radar( In ISAR) imaging algorithms of ship targets w ith 2-D sparsity in actual radar imaging system. To deal w ith this problem,a novel 3-D In ISAR imaging method is proposed in this paper.First,the high-precision gradient adaptive algorithm w as adopted to reconstruct the echoes in range dimension. Then the method of minimizing the entropy of the average range profile w as applied to estimate the parameters w hich are used to compensate translation components of the received echoes. Besides,the phase adjustment and image coregistration of the sparse echoes w ere achieved at the same time through the approach of the joint phase autofocus. Finally,the 3-D geometry coordinates of the ship target w ith 2-D sparsity w ere reconstructed by combining the range measurement and interferometric processing of the ISAR images. Simulation experiments w ere carried out to verify the practicability and effectiveness of the algorithm in the case that the received echoes are in 2-D sparsity.
