Arbitrarily high-order accurate simulations of compressible rotationally constrained convection using a transfinite mapping on cubed-sphere grids

Chen, Kuangxu1; Liang, Chunlei1; Wan, Minping2,3

2023-08-01

10.1063/5.0158146

PHYSICS OF FLUIDS   影响因子和分区

1070-6631

1089-7666

We present two major improvements over the Compressible High-ORder Unstructured Spectral difference (CHORUS) code published in Wang et al., "A compressible high-order unstructured spectral difference code for stratified convection in rotating spherical shells," J. Comput. Phys. 290, 90-111 (2015). The new code is named CHORUS++ in this paper. Subsequently, we perform a series of efficient simulations for rotationally constrained convection (RCC) in spherical shells. The first improvement lies in the integration of the high-order spectral difference method with a boundary-conforming transfinite mapping on cubed-sphere grids, thus ensuring exact geometric representations of spherical surfaces on arbitrary sparse grids. The second improvement is on the adoption of higher-order elements (sixth-order) in CHORUS++ vs third-order elements for the original CHORUS code. CHORUS++ enables high-fidelity RCC simulations using sixth-order elements on very coarse grids. To test the accuracy and efficiency of using elements of different orders, CHORUS++ is applied to a laminar solar benchmark, which is characterized by columnar banana-shaped convective cells. By fixing the total number of solution degrees of freedom, the computational cost per time step remains unchanged. Nevertheless, using higher-order elements in CHORUS++ resolves components of the radial energy flux much better than using third-order elements. To obtain converged predictions, using sixth-order elements is 8.7 times faster than using third-order elements. This significant speedup allows global-scale fully compressible RCC simulations to reach equilibration of the energy fluxes on a small cluster of just 40 cores. In contrast, CHORUS simulations were performed by Wang et al. on supercomputers using approximately 10 000 cores. Using sixth-order elements in CHORUS++, we further carry out global-scale solar convection simulations with decreased rotational velocities. Interconnected networks of downflow lanes emerge and surround broader and weaker regions of upflow fields. A strong inward kinetic energy flux compensated by an enhanced outward enthalpy flux appears. These observations are all consistent with those published in the literature. Furthermore, CHORUS++ can be extended to magnetohydrodynamic simulations with potential applications to the hydromagnetic dynamo processes in the interiors of stars and planets.

SCI ; EI

英语

通讯

National Science Foundation (NSF) CAREER Award[1952554] ; Air Force Office of Scientific Research (AFOSR) grant[FA9550-20-1-0374] ; NSFC[12225204] ; Department of Science and Technology of Guangdong Province[2020B1212030001] ; Shenzhen Science and Technology Program[KQTD20180411143441009]

Mechanics ; Physics

Mechanics ; Physics, Fluids & Plasmas

WOS:001049438800002

AIP Publishing

20233514638674

Degrees of freedom (mechanics) ; Kinetic energy ; Kinetics ; Magnetohydrodynamics ; Photomapping ; Supercomputers

Surveying:405.3 ; Magnetohydrodynamics (MHD) Power Generation:615.3 ; Fluid Flow, General:631.1 ; Digital Computers and Systems:722.4 ; Photography:742.1 ; Classical Physics; Quantum Theory; Relativity:931 ; Mechanics:931.1

PHYSICS

Web of Science

1.Clarkson Univ, Dept Mech & Aerosp Engn, Potsdam, NY 13699 USA
2.Southern Univ Sci & Technol, Dept Mech & Aerosp Engn, Guangdong Prov Key Lab Turbulence Res & Applicat, Shenzhen 518055, Peoples R China
3.Southern Univ Sci & Technol, Guangdong Hong Kong Macao Joint Lab Data Driven Fl, Hong Kong 518055, Guangdong, Peoples R China

Chen, Kuangxu,Liang, Chunlei,Wan, Minping. Arbitrarily high-order accurate simulations of compressible rotationally constrained convection using a transfinite mapping on cubed-sphere grids[J]. PHYSICS OF FLUIDS,2023,35(8).

Chen, Kuangxu,Liang, Chunlei,&Wan, Minping.(2023).Arbitrarily high-order accurate simulations of compressible rotationally constrained convection using a transfinite mapping on cubed-sphere grids.PHYSICS OF FLUIDS,35(8).

Chen, Kuangxu,et al."Arbitrarily high-order accurate simulations of compressible rotationally constrained convection using a transfinite mapping on cubed-sphere grids".PHYSICS OF FLUIDS 35.8(2023).