  A general framework for the development of high-order compact schemes has
been proposed recently. The core steps of the schemes are composed of the
following. 1). Based on a kinetic model equation, from a generalized initial
distribution of flow variables construct a time-accurate evolution solution of
gas distribution function at a cell interface ; 2). Introduce the WENO-type
weighting functions into the time-derivative of the cell interface flux
function in the multistage multi-derivative time stepping scheme to cope with
the possible impingement of a shock wave on a cell interface within a time
step; 3). Take moments of interface gas distribution function to obtain the
time-accurate flow variables and the corresponding fluxes at the cell
interface, and update the cell-averaged flow variables and their gradients
inside each control volume; 4). Within the physical domain of dependence of the
reconstructed cell, based on the cell-averaged flow variables and their
gradients develop compact initial data reconstruction to get initial flow
distributions at the beginning of next time step. A compact gas-kinetic scheme
(GKS) up to sixth-order accuracy in space and fourth-order in time has been
constructed on 2D unstructured mesh before. In this paper, the compact GKS up
to fourth-order accuracy on 3D tetrahedral mesh will be further constructed
with the focus on the WENO-type initial data reconstruction. Nonlinear weights
are designed to achieve high-order accuracy for the smooth Navier-Stokes
solution and keep super robustness in 3D computation with strong shock
interactions. The fourth-order compact GKS can use a large time step with CFL
number $0.6$ in the simulations from subsonic to hypersonic flow. A series of
test cases are used to validate the scheme. The high-order compact GKS is ready
for 3D applications with complex geometry.
